Athanassios S. Fokas

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Mathematics

#905

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#1590

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Applied Mathematics

#19

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#22

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Measure Theory

#414

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#600

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Mathematics

Why Is Athanassios S. Fokas Influential?

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According to Wikipedia, Athanassios Spyridon Fokas is a Greek mathematician, with degrees in Aeronautical Engineering and Medicine. Since 2002, he is Professor of Nonlinear Mathematical Science in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge.

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Athanassios S. Fokas's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Symplectic structures, their B?acklund transformation and hereditary symmetries (1981) (1632)
Complex Variables: Introduction and Applications (1997) (653)
A unified transform method for solving linear and certain nonlinear PDEs (1997) (516)
On a class of physically important integrable equations (1994) (469)
The isomonodromy approach to matric models in 2D quantum gravity (1992) (441)
A Unified Approach To Boundary Value Problems (2008) (397)
Painleve Transcendents: The Riemann-hilbert Approach (2006) (396)
The Isomonodromy Approach to Matrix Models in 2 D Quantum Gravity (2004) (363)
Discrete Painlevé equations and their appearance in quantum gravity (1991) (296)
Integrable Nonlinear Evolution Equations on the Half-Line (2002) (281)
Generating mechanism for higher-order rogue waves. (2012) (272)
On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation (1983) (266)
Symmetries and Integrability (1987) (253)
On the inverse scattering transform of multidimensional nonlinear equations related to first‐order systems in the plane (1984) (235)
A symmetry approach to exactly solvable evolution equations (1980) (233)
Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation (2016) (225)
Complex Variables: Contents (2003) (221)
On a unified approach to transformations and elementary solutions of Painlevé equations (1982) (203)
Recursion operators and bi-Hamiltonian structures in multidimensions. I (1988) (202)
On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation (1983) (190)
The hierarchy of the Benjamin-Ono equation (1981) (175)
The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems (1983) (175)
Mathematical Physics 2000 (2000) (175)
Important developments in soliton theory (1993) (167)
The nonlinear Schrödinger equation on the half-line (2004) (163)
On the integrability of linear and nonlinear partial differential equations (2000) (146)
Linearization of the Korteweg-de Vries and Painlevé II Equations (1981) (140)
On the exactly solvable equation$S_t = [ ( \beta S + \gamma )^{ - 2} S_x ]_x + \alpha ( \beta S + \gamma )^{ - 2} S_x $ Occurring in Two-Phase Flow in Porous Media (1982) (137)
From Continuous to Discrete Painlevé Equations (1993) (136)
The linearization of the initial-boundary value problem of the nonlinear Schro¨dinger equation (1996) (133)
On the structure of symplectic operators and hereditary symmetries (1980) (131)
On a novel integrable generalization of the nonlinear Schrödinger equation (2008) (130)
On a new non-local formulation of water waves (2006) (126)
Two–dimensional linear partial differential equations in a convex polygon (2001) (118)
On the solvability of Painlevé II and IV (1992) (116)
On the solvability of the N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations (1992) (115)
An initial-boundary value problem for the nonlinear Schrödinger equation (1989) (113)
Surfaces on Lie groups, on Lie algebras, and their integrability (1996) (112)
The unified method: I. Nonlinearizable problems on the half-line (2011) (111)
On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems (1982) (110)
A new transform method for evolution partial differential equations (2002) (108)
An integrable generalization of the nonlinear Schrödinger equation on the half-line and solitons (2008) (101)
Integrable nonlinear evolution partial differential equations in 4 + 2 and 3 + 1 dimensions. (2006) (99)
The unique determination of neuronal currents in the brain via magnetoencephalography (2004) (97)
Bäcklund transformations for hereditary symmetries (1981) (95)
Analysis of the Global Relation for the Nonlinear Schrödinger Equation on the Half-line (2003) (94)
The generalized Dirichlet‐to‐Neumann map for certain nonlinear evolution PDEs (2005) (93)
THE mKdV EQUATION ON THE HALF-LINE (2004) (92)
Hodograph transformations of linearizable partial differential equations (1989) (91)
Interaction of lumps with a line soliton for the DSII equation (2001) (90)
The nonlinear Schrödinger equation on the interval (2004) (90)
A transform method for linear evolution PDEs on a finite interval (2004) (86)
The recursion operator of the Kadomtsev-Petviashvili equation and the squared eigenfunctions of the Schrödinger operator (1986) (86)
Dynamically stretched vortices as solutions of the 3D Navier—Stokes equations (1999) (81)
Integrable Nonlinear Evolution Equations on a Finite Interval (2006) (80)
Rogue waves of the nonlocal Davey–Stewartson I equation (2018) (79)
Integrability of linear and nonlinear evolution equations and the associated nonlinear fourier transforms (1994) (78)
INVERSE SCATTERING OF FIRST ORDER SYSTEMS IN THE PLANE RELATED TO NONLINEAR MULTIDIMENSIONAL EQUATIONS (1983) (76)
The unified method: II. NLS on the half-line with t-periodic boundary conditions (2011) (75)
The Korteweg-de Vries equation and beyond (1995) (74)
Generalized conditional symmetries and exact solutions of non-integrable equations (1994) (73)
On the initial value problem of the second Painlevé Transcendent (1983) (72)
On the simplest integrable equation in 2+1 (1994) (71)
Highly Oscillatory Problems (2009) (70)
A formula for constructing infinitely many surfaces on Lie algebras and integrable equations (2000) (69)
The dressing method and nonlocal Riemann-Hilbert problems (1992) (68)
Method of Solution for a Class of Multidimensional Nonlinear Evolution Equations (1983) (67)
An analytical solution for linear waterflood including the effects of capillary pressure (1983) (67)
A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods (2008) (62)
A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line (2008) (62)
Hamiltonian theory over noncommutative rings and integrability in multidimensions (1992) (62)
Synthesis, as Opposed to Separation, of Variables (2012) (61)
On a transform method for the Laplace equation in a polygon (2003) (60)
Mathematical model of granulocytopoiesis and chronic myelogenous leukemia. (1991) (60)
A Plethora of Integrable Bi-Hamiltonian Equations (1997) (57)
Forced Nonlinear Evolution Equations and the Inverse Scattering Transform (1989) (57)
An analytical method for linear elliptic PDEs and its numerical implementation (2004) (56)
A method of linearization for Painleve´ equations: Painleve´ IV, V (1988) (56)
A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon (2010) (56)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: The isomonodromy approach in the theory of two-dimensional quantum gravitation (1990) (56)
On the non-uniqueness of the inverse MEG problem (2005) (56)
The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation (2008) (55)
The inverse scattering transform for multidimensional (2+1) problems (1983) (54)
Quadratic and cubic invariants in classical mechanics (1980) (53)
ON THE INVERSE SCATTERING AND DIRECT LINEARIZING TRANSFORMS FOR THE KADOMTSEV-PETVIASHVILI EQUATION (1983) (52)
Inversion method for magnetoencephalography (1996) (52)
On a novel integrable generalization of the sine-Gordon equation (2010) (49)
Mathematical models and deep learning for predicting the number of individuals reported to be infected with SARS-CoV-2 (2020) (48)
An initial-boundary value problem for the sine-Gordon equation in laboratory coordinates (1992) (48)
Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations (2000) (48)
On the asymptotic analysis of the Painlevé equations via the isomonodromy method (1994) (46)
The direct linearization of a class of nonlinear evolution equations (1984) (44)
Unified Transform for Boundary Value Problems: Applications and Advances (2014) (44)
Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations (2008) (44)
The basic elliptic equations in an equilateral triangle (2004) (44)
The unified method: III. Nonlinearizable problems on the interval (2011) (43)
Electro-magneto-encephalography for a three-shell model: dipoles and beyond for the spherical geometry (2009) (42)
Algebraic Aspects of Integrable Systems (1996) (42)
Bi‐Hamiltonian formulation of the Kadomtsev–Petviashvili and Benjamin–Ono equations (1988) (42)
Two-point boundary value problems for linear evolution equations (2001) (42)
Explicit integral solutions for the plane elastostatic semi-strip (2004) (41)
On the complementarity of electroencephalography and magnetoencephalography (2007) (41)
Explicit soliton asymptotics for the Korteweg–de Vries equation on the half-line (2008) (41)
Boundary-value problems for the stationary axisymmetric Einstein equations: a rotating disc (2010) (41)
An initial-boundary value problem for the Korteweg-de Vries equation (1994) (40)
Solving PDEs of fractional order using the unified transform method (2018) (40)
Soliton cellular automata (1990) (40)
Boundary Value Problems for Boussinesq Type Systems (2005) (40)
Rogue wave management in an inhomogeneous Nonlinear Fibre with higher order effects (2013) (39)
Water waves over a variable bottom: a non-local formulation and conformal mappings (2012) (39)
A non-local formulation of rotational water waves (2008) (38)
On the solvability of Painlevé ${\rm II}$ and ${\rm IV}$ (1992) (38)
Solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence. (2001) (37)
The Fundamental Differential Form and Boundary‐Value Problems (2002) (37)
Electro–magneto-encephalography for a three-shell model: distributed current in arbitrary, spherical and ellipsoidal geometries (2009) (36)
The Korteweg–de Vries equation on the half-line (2016) (36)
Interaction of simple particles in soliton cellular automata (1989) (36)
A semi-analytical numerical method for solving evolution and elliptic partial differential equations (2009) (35)
Integrability and Self-Similarity in Transient Stimulated Raman Scattering (1999) (35)
A new transform method I: domain-dependent fundamental solutions and integral representations (2010) (34)
Inverse scattering transform for the KPI equation on the background of a one-line soliton*Inverse scattering transform for the KPI equation on the background of a one-line soliton (2003) (34)
On the limit from the intermediate long wave equation to the Benjamin–Ono equation (1984) (33)
Reconstruction algorithm for single photon emission computed tomography and its numerical implementation (2006) (33)
Linearizable initial boundary value problems for the sine-Gordon equation on the half-line (2004) (33)
Initial–boundary value problems associated with the Ablowitz–Ladik system (2017) (32)
A Hele-Shaw problem and the second Painlevé transcendent (1998) (31)
The Cauchy problem for the Kadomtsev–Petviashvili–I equation without the zero mass constraint (1999) (31)
The bi‐Hamiltonian formulation of the Landau–Lifshiftz equation (1988) (31)
The modified Helmholtz equation in a semi-strip (2005) (30)
On the periodic intermediate long wave equation (1982) (30)
The Dirichlet-to-Neumann map for the elliptic sine-Gordon equation (2012) (30)
Localised coherent solutions of the DSI and DSII equations - a numerical study (2005) (30)
The solution of certain initial boundary-value problems for the linearized Korteweg—deVries equation (1998) (30)
The nonlinear Schrödinger equation with t-periodic data: I. Exact results (2014) (29)
Evolution Theory, Periodic Particles, and Solitons in Cellular Automata† (1989) (29)
The Generalized Dirichlet to Neumann Map for the KdV Equation on the Half-Line (2006) (29)
Generalized Dirichlet to Neumann map for moving initial-boundary value problems (2006) (28)
A new transform method II: the global relation and boundary-value problems in polar coordinates (2010) (28)
Exact interaction of solitary waves for certain nonintegrable equations (1996) (27)
The Dbar formalism for certain linear non-homogeneous elliptic PDEs in two dimensions (2006) (27)
Evolution of methacrylate distribution during wood saturation (2005) (27)
Recursion operators and bi-Hamiltonian structures in multidimensions. II (1988) (27)
Generalized Fourier Transforms , Their Nonlinearization and the Imaging of the Brain (2005) (26)
The Solution of the modified Helmholtz equation in a wedge and an application to diffusion-limited coalescence (1999) (26)
The scaling reduction of the three-wave resonant system and the Painlevé VI equation (1986) (26)
The Dirichlet-to-Neumann map for the heat equation on a moving boundary (2007) (25)
The Davey-Stewartson Equation on the Half-Plane (2009) (25)
Coherent structures in cellular automata (1990) (25)
Schlesinger transformations of Painlevé II‐V (1992) (25)
Order and the ubiquitous occurrence of chaos (1996) (24)
Davey-Stewartson type equations in 4+2 and 3+1 possessing soliton solutions (2013) (24)
The nonlinear Schrödinger equation with t-periodic data: II. Perturbative results (2014) (24)
Nonlinear processes in physics (1993) (24)
A numerical technique for linear elliptic partial differential equations in polygonal domains (2015) (24)
Doubly Localized Two-Dimensional Rogue Waves in the Davey–Stewartson I Equation (2021) (23)
Integral transforms, spectral representation and the d-bar problem (2000) (22)
The definite non-uniqueness results for deterministic EEG and MEG data (2013) (22)
Discrete analogues of δ-equation and of Radon transform (1991) (22)
Proof of some asymptotic results for a model equation for low Reynolds number flow (1978) (22)
Inverse problem for N × N hyperbolic systems on the plane and the N-wave interactions (1991) (22)
Equations of motion of self-gravitatingN-body systems in the first post-Minkowskian approximation (2018) (22)
The Heat Equation in the Interior of an Equilateral Triangle (2010) (22)
Conformal Mappings to Multiply Connected Polycircular Arc Domains (2012) (21)
Electro-magneto-encephalography for the three-shell model: numerical implementation via splines for distributed current in spherical geometry (2012) (21)
Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman (2011) (21)
Initial Boundary-Value Problems for Soliton Equations (1993) (20)
Lax pairs and a new spectral method for linear and integrable nonlinear PDEs (1998) (20)
On the structure, masses and thermodynamics of the W±± bosons (2016) (20)
On the construction of evolution equations admitting a master symmetry (2001) (20)
Boundary Value Problems for the Elliptic Sine-Gordon Equation in a Semi-strip (2009) (19)
A Riemann–Hilbert Approach to the Laplace Equation (2000) (19)
The unified transform for mixed boundary condition problems in unbounded domains (2019) (19)
PARALLEL LINE ROGUE WAVES OF THE THIRD-TYPE DAVEY-STEWARTSON EQUATION (2016) (19)
Boundary-value problems for linear PDEs with variable coefficients (2004) (18)
Matrix models of two-dimensional quantum gravity and isomonodromic solutions of “discrete Painlevé” equations (1995) (18)
The Inverse Spectral Method for Colliding Gravitational Waves (1998) (18)
A quantitative framework for exploring exit strategies from the COVID-19 lockdown (2020) (18)
Comments on the inverse scattering transform and related nonlinear evolution equations (1983) (18)
An inverse problem for multidimensional first‐order systems (1986) (17)
The direct linearizing transform and the Benjamin-Ono equation (1983) (17)
Conformal mappings to a doubly connected polycircular arc domain (2007) (17)
Integrable functional equations and algebraic geometry (1994) (17)
Group theoretical aspects of constants of motion and separable solutions in classical mechanics (1979) (16)
Lax pairs: a novel type of separability (2009) (16)
Strict rules determine arrangements of strands in sandwich proteins. (2006) (16)
Absolute and Convective Instability for Evolution PDEs on the Half‐Line (2005) (16)
Particles in Soliton Cellular Automata (1989) (16)
A Bohr-type model with gravity as the attractive force (2013) (16)
A hybrid analytical-numerical method for solving advection-dispersion problems on a half-line (2019) (16)
Bi-Hamiltonian Structures and Integrability (1993) (15)
The unified method for the heat equation: I. non-separable boundary conditions and non-local constraints in one dimension (2013) (15)
Complexification and integrability in multidimensions (2018) (15)
Eigenvalues for the Laplace Operator in the Interior of an Equilateral Triangle (2014) (15)
Electroencephalography and Magnetoencephalography (2020) (15)
The Modified Korteweg-de Vries Equation on the Half-Line with a Sine-Wave as Dirichlet Datum (2013) (15)
Methods for Solving Elliptic PDEs in Spherical Coordinates (2008) (15)
A geometric construction determines all permissible strand arrangements of sandwich proteins. (2005) (14)
Quaternions, Evaluation of Integrals and Boundary Value Problems (2007) (14)
Evolution PDEs and augmented eigenfunctions. Finite interval (2013) (14)
Infinitely many commuting symmetries and constants of motion in involution for explicitly time‐dependent evolution equations (1984) (14)
Soliton multidimensional equations and integrable evolutions preserving Laplace's equation (2008) (14)
Long‐time asymptotics of moving boundary problems using an Ehrenpreis‐type representation and its Riemann‐Hilbert nonlinearization (2003) (13)
Well-Posedness of an Integrable Generalization of the Nonlinear Schrödinger Equation on the Circle (2011) (13)
Note on solutions to a class of nonlinear singular integro-differential equations (1987) (13)
Easing COVID-19 lockdown measures while protecting the older restricts the deaths to the level of the full lockdown (2020) (13)
Evaluation of a spline reconstruction technique: Comparison with FBP, MLEM and OSEM (2010) (13)
The Inverse Spectral Theory for the Ward Equation and for the 2+1 Chiral Model (1998) (13)
Evaluation of the spline reconstruction technique for PET. (2014) (12)
Analytical computation of the Mercury perihelion precession via the relativistic gravitational law and comparison with general relativity (2015) (12)
Predictive mathematical models for the number of individuals infected with COVID-19 (2020) (12)
On the initial value problem for a class of nonlinear integral evolution equations including the sine-Hilbert equation (1987) (12)
Zero-dispersion limit for integrable equations on the half-line with linearisable data (2004) (12)
The Isomonodromy Method and the Painlevé Equations (1993) (12)
Group theoretical nature of Bäcklund transformations (1979) (12)
Generalized symmetries and constants of motion of evolution equations (1979) (11)
Generalized Dirichlet‐to‐Neumann Map in Time‐Dependent Domains (2012) (11)
Integrable evolution equations in time-dependent domains (2001) (11)
Invariants, Lie-Bäcklund operators and Bäcklund transformations (1979) (11)
Prediction of the structural motifs of sandwich proteins. (2004) (11)
Electro-magneto-encephalography for the three-shell model: minimal L2-norm in spherical geometry (2012) (11)
Nonlinear integrable equations and nonlinear Fourier transform (1995) (11)
Highlights of mathematical physics (2002) (10)
The Time Periodic Solution of the Burgers Equation on the Half-Line and an Application to Steady Streaming (2004) (10)
On the mass and thermodynamics of the Higgs boson (2018) (10)
Poisson Brackets for Integrable Lattice Systems (1996) (10)
On the structure, mass and thermodynamics of the Zo bosons (2016) (10)
The Poisson and the Biharmonic Equations in the Interior of a Convex Polygon (2015) (10)
Electro‐magneto‐encephalography for the three‐shell model : a single dipole in ellipsoidal geometry (2012) (10)
Nonlinear Fourier transforms, integrability and nonlocality in multidimensions (2007) (10)
Catalysis and autocatalysis of chemical synthesis and of hadronization (2017) (10)
The D-bar method, inversion of certain integrals and integrability in 4 + 2 and 3 + 1 dimensions (2008) (10)
Global solutions and their asymptotic behavior for Benjamin-Ono-Burgers type equations (2000) (9)
The Kadomtsev-Petviashvili II equation on the half-plane (2010) (9)
Continuous and Discrete Painlevé Equations (1992) (9)
The attenuated spline reconstruction technique for single photon emission computed tomography (2018) (9)
LAPLACE'S EQUATION IN THE EXTERIOR OF A CONVEX POLYGON. THE EQUILATERAL TRIANGLE (2010) (9)
The Unified Method in Polygonal Domains via the Explicit Fourier Transform of Legendre Polynomials (2013) (9)
Inverse problems in multidimensions (1991) (8)
Elliptic boundary value problems in convex polygons with low regularity boundary data via the unified method (2013) (8)
A novel method of solution for the fluid-loaded plate (2008) (8)
Asymptotics to all orders of the Hurwitz zeta function (2017) (8)
Quadratic Poisson algebras and their infinite‐dimensional extensions (1994) (8)
Integrable equations on the half-infinite line (1995) (8)
Boundary value problems for systems of linear evolution equations (2004) (7)
Fokas method for linear boundary value problems involving mixed spatial derivatives (2020) (7)
Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons (2018) (7)
A new approach to integrable evolution equations on the circle (2021) (7)
The Davey–Stewartson I equation on the quarter plane with homogeneous Dirichlet boundary conditions (2003) (7)
Electro-magneto-encephalography and fundamental solutions (2009) (7)
Elliptic equations with low regularity boundary data via the unified method (2015) (7)
Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period (2021) (7)
An iterative spatial-stepping numerical method for linear elliptic PDEs using the Unified Transform (2019) (7)
Multi-Solitons, Multi-Breathers and Multi-Rational Solutions of Integrable Extensions of the Kadomtsev–Petviashvili Equation in Three Dimensions (2022) (7)
COVID-19: Predictive Mathematical Models for the Number of Deaths in South Korea, Italy, Spain, France, UK, Germany, and USA (2020) (7)
Kadomtsev–Petviashvili Equation Revisited and Integrability in 4 + 2 and 3 + 1 (2009) (7)
The unified transform for the heat equation: II. Non-separable boundary conditions in two dimensions (2015) (7)
On the asymptotic integrability of a higher‐order evolution equation describing internal waves in a deep fluid (1996) (6)
Two alternative scenarios for easing COVID-19 lockdown measures: one reasonable and one catastrophic (2020) (6)
On the use of Lie-Bäcklund operators in quantum mechanics (1980) (6)
Nonlinear Processes in Physics: Proceedings of the III Potsdam--V Kiev Workshop at Clarkson University, Potsdam, New York, August 1-11, 1991 (1991) (6)
A UNIFIED APPROACH TO RECURSION OPERATORS (1990) (6)
Electro-Magneto-Encephalography for the three-Shell Model: Numerical Implementation for Distributed Current in Spherical Geometry (2009) (6)
A transform method for evolution PDEs on a finite interval (2008) (6)
Electro-magnetoencephalography for a spherical multiple-shell model: novel integral operators with singular-value decompositions (2020) (6)
Highly Oscillatory Problems: Novel analytical and numerical methods for elliptic boundary value problems (2009) (6)
The SRT reconstruction algorithm for semiquantification in PET imaging. (2015) (6)
A new immersion formula for surfaces on Lie algebras and integrable equations (2001) (5)
The Laplace equation in the exterior of the Hankel contour and novel identities for hypergeometric functions (2012) (5)
Evaluation of a Spline Reconstruction Technique for SPECT: Comparison with FBP and OSEM (2011) (5)
On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function (2012) (5)
Systematic construction and prediction of the arrangement of the strands of sandwich proteins (2009) (5)
Hamiltonians and conjugate Hamiltonians of some fourth-order nonlinear ODEs (2012) (5)
A novel approach to the Lindelöf hypothesis (2019) (5)
Complex Variables: Preface (2003) (5)
The unified transform for linear, linearizable and integrable nonlinear partial differential equations (2014) (5)
The Fourier Transforms of the Chebyshev and Legendre Polynomials (2012) (5)
SARS-CoV-2: The Second Wave in Europe (2021) (5)
Water waves with moving boundaries (2017) (5)
On a Novel Class of integrable ODEs Related to the Painlevé equations (2010) (5)
THE UNIFIED TRANSFORM FOR THE MODIFIED HELMHOLTZ EQUATION IN THE EXTERIOR OF A SQUARE (2014) (5)
The implementation of the unified transform to the nonlinear Schrödinger equation with periodic initial conditions (2021) (5)
The bi-Hamiltonian formulations of integrable evolution equations in multidimensions (1987) (5)
Fractal analysis of tree paintings by Piet Mondrian (1872-1944) (2017) (5)
Boundary value problems for the stationary axisymmetric Einstein equations: a rotating disk (2009) (5)
Relations between the baryon quantum numbers of the Standard Model and of the rotating neutrino model (2016) (4)
Evolution equations on time-dependent intervals (2019) (4)
Analytical reconstructions for PET and spect employing L1-denoising (2009) (4)
The Mathematics of the Imaging Techniques of MEG, CT, PET and SPECT (2006) (4)
The dressing method, symmetries, and invariant solutions (1990) (4)
The Inverse Spectral Method on the Plane (1993) (4)
Gravitational mass and Newton's universal gravitational law under relativistic conditions (2015) (4)
EEG for Current With Two-Dimensional Support (2018) (4)
Aspects of Integrability in One and Several Dimensions (1986) (4)
The Unified Transform: A Spectral Collocation Method for Acoustic Scattering (2019) (4)
Helmholtz decomposition of the neuronal current for the ellipsoidal head model (2018) (4)
On Two Useful Identities in the Theory of Ellipsoidal Harmonics (2009) (4)
Generalized Fourier Transforms, Inverse Problems, and Integrability in 4+2 (2009) (4)
Reconstruction Algorithms for Positron Emission Tomography and Single Photon Emission Computed Tomography and their Numerical Implementation (2004) (4)
Uniform asymptotics as a stationary point approaches an endpoint (2017) (4)
Computation of masses and binding energies of some hadrons and bosons according to the rotating lepton model and the relativistic Newton equation (2016) (4)
Linearisable nonlinear partial differential equations in multidimensions (2015) (4)
Emerging Patterns and Computational Design of Filter Cellular Automata (1993) (4)
Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products (2018) (4)
A formal proof of Lindel\"of's hypothesis (2017) (3)
On the asymptotic linearization of acoustic waves (2008) (3)
A formal proof of a slight variant of Lindel\"of's hypothesis (2017) (3)
The Initial-Boundary Value Problem for the Davey-Stewartson 1 Equation; How to Generate and Drive Localized Coherent Structures in Multidimensions (1990) (3)
A Numerical Technique for Linear Elliptic PDEs in Polygonal Domains (2015) (3)
Lectures on the Theory of Water Waves: A Novel Non-Local Formulation of Water Waves (2016) (3)
A hybrid analytical–numerical algorithm for determining the neuronal current via electroencephalography (2020) (3)
Generalised Dirichlet to Neumann maps for linear dispersive equations on half-line (2014) (3)
A Method of Solution for Painleve Equations: Painleve IV, V, (1987) (3)
Explicit asymptotics for certain single and double exponential sums (2017) (3)
Direct linearizations of the Korteweg‐deVries equations (1982) (3)
Linear Elliptic PDEs in a Cylindrical Domain with a Polygonal Cross‐Section (2017) (3)
Integrable Equations with a Forcing of a Distribution Type (1994) (2)
On the Initial Value Problem of the Third Painlevé Equation (1990) (2)
The unified transform for evolution equations on the half‐line with time‐periodic boundary conditions * (2021) (2)
Ultra-relativistic gravity has properties associated with the strong force (2019) (2)
New Manifestations of Solitons (1990) (2)
Integrable Systems and the Inverse Scattering Method (2006) (2)
A direct linearization associated with the Benjamin‐Ono equation (1982) (2)
ALTERNATING REGULARISATION IN MEASUREMENT-AND IMAGE SPACE FOR PET RECONSTRUCTION (2011) (2)
On the Asymptotics of the Riemann Zeta Function to all Orders (2012) (2)
Integrable Nonlinear Equations (1992) (2)
Accounting for super-spreader events and algebraic decay in SIR models (2022) (2)
A Novel Integral Equation for the Riemann Zeta Function and Large t-Asymptotics (2019) (2)
A Novel Approach to Elastodynamics: II. The Three-Dimensional Case (2010) (2)
Ehrenpreis Type Representations and Their Riemann–Hilbert Nonlinearisation (2003) (2)
On the proof of a variant of Lindelöf's hypothesis (2017) (2)
Quantification of T1, T2 relaxation times from magnetic resonance fingerprinting radially undersampled data using analytical transformations. (2021) (1)
Boundary Value Problems in 1 + 1 and in 2 + 1, the Dressing Method, and Cellular Automata (1990) (1)
Evaluation of the spline reconstruction technique for preclinical PET imaging (2022) (1)
Uniform transform method for boundary value problems involving mixed derivatives (2020) (1)
The nonlinear Schr\"odinger equation with forcing involving products of eigenfunctions (2022) (1)
An effective approach to electromagnetoencephalography (2008) (1)
Inverse scattering problem for a hyperbolic system of first order equations on a semi-axis on a first approximation (2016) (1)
Introduction to Complex Variables and Applications (2021) (1)
An extension of integrable equations (2022) (1)
A Novel Approach to Elastodynamics: I. The Two-Dimensional Case (2010) (1)
Inverse Problems and a Unified Approach to Integrability in 1, 1+1 and 2+1 Dimensions (1988) (1)
Solitons and Dromions, Coherent Structures in a Nonlinear World (1990) (1)
Extensions of the d’Alembert formulae to the half line and the finite interval obtained via the unified transform (2022) (1)
Mathematical Methods in PET and SPECT Imaging (2015) (1)
Chapter 3: Evolution Problems: Nonlinear (2014) (1)
Gravitationally confined relativistic neutrinos (2017) (1)
Symmetries and BI-Hamiltonian Structures of 2+1 Dimensional Systems, (1986) (1)
A Residue representation for integrable equations in multidimensions (1991) (1)
Inversion of the attenuated radon transform using cubic splines (2016) (1)
Algorithmic Construction of the Recursion Operators of Toda and Landau-Lifshitz Equation(Toda Lattice and the Related Topics) (1988) (1)
Complex Variables: Residue Calculus and Applications of Contour Integration (2003) (1)
A Unified Method for Solving Linear and Nonlinear Evolution Equations and an Application to Integrable Surfaces (1996) (1)
Spectral Theory of Linear λ-Matrices and the Solution of Certain Nonlinear Algebraic and Functional Equations (1993) (1)
The Modified Helmholtz Equation on a Regular Hexagon - The Symmetric Dirichlet Problem (2020) (1)
Linear superpositions in nonlinear wave equations (1997) (1)
A New Approach for the Inversion of the Attenuated Radon Transform (2019) (1)
Perturbative and Exact Results on the Neumann Value for the Nonlinear Schrödinger on the Half-line (2014) (1)
Reconstruction of Preclinical PET Images via Chebyshev Polynomial Approximation of the Sinogram (2022) (1)
1. Evolution Equations on the Half-Line (2008) (1)
An initial-boundary value problem for the nonlinear Schrdinger equation (1989) (1)
Simple Formulae, Deep Learning and Elaborate Modelling for the COVID-19 Pandemic (2022) (1)
Inverse monodromy problem and Riemann-Hilbert factorization (2006) (1)
Correction to: Solving the Initial Value Problem for the 3-Wave Interaction Equations in Multidimensions (2021) (1)
Chapter 7: Numerical Methods for Elliptic Problems (2014) (0)
Ehrenpreis Type Representations and Their Riemann – (2003) (0)
11. The Basic Elliptic PDEs in a Polygonal Domain (2008) (0)
On the Inverse Scattering Transform in Two Spatial and One Temporal Dimensions (1983) (0)
Nonlinear waves. Technical report (1989) (0)
PIII equation, an overview (2006) (0)
14. A Collocation Method in the Fourier Plane (2008) (0)
Complex Variables: Asymptotic Evaluation of Integrals (2003) (0)
A Spline Approach to Parallel-Hole Collimator Deblurring for aSRT-Reconstructed SPECT Images (2019) (0)
Asymptotic solutions of the second Painlevé equation in the complex plane. Inverse monodromy problem approach (2006) (0)
Calculation of All Commutation Relations Among Scattering Data Without Using the R-Matrix Approach (1993) (0)
Non-Perturbative Two-Dimensional Quantum Gravity and the Isomonodromy Method (1993) (0)
8. The Dirichlet to Neumann Map for a Moving Boundary (2008) (0)
9. Divergence Formulation, the Global Relation, and Lax Pairs (2008) (0)
Evolution PDEs and augmented (2014) (0)
The Korteweg–De Vries Equation with Forcing Involving Products of Eigenfunctions (2023) (0)
A hybrid analytical-numerical algorithm for determining the neuronal current via EEG (2019) (0)
CONFERENCE IN NUMERICAL ANALYSIS (NumAn 2007) RECENT APPROACHES TO NUMERICAL ANALYSIS: THEORY, METHODS AND APPLICATIONS (2007) (0)
Mathematics, Innate Knowledge and Neuroscience, COMPLETE (2012) (0)
N T ] 5 D ec 2 01 7 Asymptotics to all orders of the Hurwitz zeta function (2018) (0)
Dynamical complexity in the C.elegans neural network (2016) (0)
Multi-resolution inversion algorithm for the attenuated radon transform (2011) (0)
Nonlinear Wave Phenomena Related to Interactions in the Ionosphere. (1993) (0)
0 61 10 09 v 2 2 2 N ov 2 00 6 The generalised Dirichlet to Neumann map for moving initial-boundary value problems (2019) (0)
Complex Variables: Sequences, Series, and Singularities of Complex Functions (2003) (0)
Which Part of the Neuronal Current can be Determined by Electroencephalography? (2020) (0)
On the proof of a variant of Lindel\"of's hypothesis (2017) (0)
Boundary Value Problems for the Elliptic Sine-Gordon Equation in a Semi-strip (2012) (0)
3. Asymptotics and a Novel Numerical Technique (2008) (0)
Solving the Initial Value Problem for the 3-Wave Interaction Equations in Multidimensions (2021) (0)
Ultra-relativistic gravity has properties associated with the strong force (2019) (0)
SARS-CoV-2: The Second Wave in Europe (Preprint) (2020) (0)
to Multiply Connected Polycircular Arc Domains (2011) (0)
Eigenvalues for the Laplace Operator in the Interior of an Equilateral Triangle (2013) (0)
A parallel unified transform solver based on domain decomposition for solving linear elliptic PDEs (2019) (0)
A Generalization of both the Method of Images and of the Classical Integral Transforms (2003) (0)
Integrable nonlinear PDEs on the half-line (2018) (0)
Supplementary material from "The attenuated spline reconstruction technique for single photon emission computed tomography" (2018) (0)
Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems (1988) (0)
5. Riemann—Hilbert and d-Bar Problems (2008) (0)
A semi-periodic initial-value problem for the Kadomtsev-Petviashvili II equation (2023) (0)
Applied Mathematics and the Imaging of the Brain (2003) (0)
PII Asymptotics on the canonical six-rays. The purely imaginary case (2006) (0)
Initial/Boundary Value Problems for Simultaneous Evolution Equations in Three Dimensions (2001) (0)
A novel approach to the Lindel\"of hypothesis. (2017) (0)
6. The Fourier Transform and Its Variations (2008) (0)
Canonical four-rays. Real-valued solutions of SG-PIII (2006) (0)
Time Perception through the Processing of Verb Tenses: An ERP study regarding Mental Time Travel (2020) (0)
Complex Variables: Complex Numbers and Elementary Functions (2003) (0)
Complex Variables: Answers to Odd-Numbered Exercises (2003) (0)
Highly Oscillatory Problems: Preface (2009) (0)
Collective properties of neural systems and their relation to other physical models (1990) (0)
An analytic reconstruction method for PET based on cubic splines (2014) (0)
Integrable nonlinear evolution equations in three spatial dimensions (2022) (0)
Complex Variables: Riemann–Hilbert Problems (2003) (0)
2. Evolution Equations on the Finite Interval (2008) (0)
Time-periodic linear boundary value problems on a finite interval (2021) (0)
A parallel unified transform solver based on domain decomposition for solving linear elliptic PDEs (2019) (0)
Complex Variables: Bibliography (2003) (0)
The implementation of the unified transform to the nonlinear Schrödinger equation with periodic initial conditions (2021) (0)
The Fourier Transforms of the Chebyshev (2012) (0)
Correction to ‘The unified transform for mixed boundary condition problems in unbounded domains’ (2019) (0)
Boundary value problems and medical imaging (2014) (0)
On the initial value problem for a class of nonlinear integral evolution equations generated through a Riemann-Hilbert spectral problem (1987) (0)
19. Asymptotics of Oscillatory Riemann—Hilbert Problems (2008) (0)
Records of Proceedings at Meetings (1998) (0)
17. Linearizable Boundary Conditions (2008) (0)
Recent Developments in Multidimensional Inverse Scattering (1991) (0)
PII Quasi-linear stokes phenomenon (2006) (0)
TheCauchyproblemfortheKadomtsev-Petviashvili-Iequation withoutthezeromassconstraint (1999) (0)
Asymptotic Methods in Nonlinear Wave Theory (A. Jeffrey and T. Kawahara) (1984) (0)
The dbar method: a tool for solving two-dimensional integrable evolution PDEs (2003) (0)
12. The New Transform Method for Elliptic PDEs in Simple Polygonal Domains (2008) (0)
A P ] 1 0 A ug 2 01 9 Evolution equations on time-dependent intervals (2019) (0)
13. Formulation of Riemann—Hilbert Problems (2008) (0)
The Unified Transform and the Water Wave Problem (2019) (0)
15. From Linear to Integrable Nonlinear PDEs (2008) (0)
Inverse scattering transform, inverse data and nonlinear evolution equations in multidimensions (1987) (0)
Preface: Mark J. Ablowitz, nonlinear waves and integrable systems. Part I (2016) (0)
Preface: Mark J. Ablowitz, nonlinear waves and integrable systems. Part II (2016) (0)
Gravitationally Confined Relativistic Neutrinos and Mathematical Modeling of the Structure of Pions (2017) (0)
Linearized Maps for the Davey-Stewartson I (1989) (0)
Canonical four-rays. Singular solutions of the SG-PIII (2006) (0)
Linearized maps for the Davey-Stewartson I equation (1989) (0)
Estimation of the neuronal current via Electro-MagnetoEncephalography using real data (2014) (0)
Integrability and beyond (1999) (0)
10. Rederivation of the Integral Representations on the Half-Line and the Finite Interval (2008) (0)
The Focusing NLS Equation on the Half-Line with Periodic Boundary Conditions (2007) (0)
PII Asymptotics on the canonical six-rays. real-valued case (2006) (0)
The isomonodromy method (2006) (0)
T Proof JIMJBoutetdeMonvel 28 May 2003 THE mKdV EQUATION ON THE HALF-LINE (2003) (0)
Piecewise Polynomial Inversion of the Radon Transform in Three Space Dimensions via Plane Integration and Applications in Positron Emission Tomography (2021) (0)
Numerical Evaluation of Fokas’ Transform Solution of the Heat Equation on the Half-Line (2017) (0)
III Potsdam-V Kiev International Workshop on Nonlinear Processes in Physics. Held in Potsdam, New York on August 1-11, 1991 (1991) (0)
4. From PDEs to Classical Transforms (2008) (0)
Dromions, a New Manifestation in Nonlinear Phenomena (1990) (0)
Asymptotics in the complex plane of the SG-PIII transcendent (2006) (0)
Symmetries and Integrability of Difference Equations: A new spectral transform for solving the continuous and spatially discrete heat equations on simple trees (1999) (0)
Isomonodromy deformations. The Painlevé equations (2006) (0)
Generalized Dirichlet to Neumann Maps for Linear Evolution Equations on Half-Line (2014) (0)
The interplay of the concrete and general: from PDEs to medical imaging (2014) (0)
7. The Inversion of the Attenuated Radon Transform and Medical Imaging (2008) (0)
Boundary value problems, medical imaging and the asymptotics of Riemann’s zeta function (2020) (0)
Systems of linear ordinary differential equations with rational coefficients. Elements of the general theory (2006) (0)
16. Nonlinear Integrable PDEs on the Half-Line (2008) (0)
Complex Variables: Analytic Functions and Integration (2003) (0)
Boundary Value Problems for Systems of Evolution Equations and an Application to Boussinesq Type Systems (1999) (0)
Comments on the symmetry structure of bi-Hamiltonian systems (1982) (0)
Complex Variables: Applications of Complex Function Theory (2003) (0)
Sine-Gordon reduction of PIII (2006) (0)
Linearizable boundary value problems for the elliptic sine-Gordon and the elliptic Ernst equations (2020) (0)
aSRT: A new analytic reconstruction algorithm for SPECT (2016) (0)
Complex Variables: Fundamentals and Techniques of Complex Function Theory (2003) (0)
Monodromy theory and special functions (2006) (0)
Sigmoid and Beyond: Algebraic Activation Functions for Artificial Neural Networks Based on Solutions of a Riccati Equation (2022) (0)
Complex Variables: Conformal Mappings and Applications (2003) (0)
The Unified Transform Method for Linear PDEs (2015) (0)
METHODS FOR SOLVING ELLIPTIC PDEs IN SPHERICAL (2008) (0)
18. The Generalized Dirichlet to Neumann Map (2008) (0)

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