Peter A. Clarkson

Peter A. Clarkson's AcademicInfluence.com Rankings

Peter A. Clarkson

Computer Science

#6352

World Rank

#6699

Historical Rank

Computational Linguistics

#1074

World Rank

#1088

Historical Rank

Machine Learning

#2032

World Rank

#2058

Historical Rank

Artificial Intelligence

#2286

World Rank

#2325

Historical Rank

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Computer Science

Peter A. Clarkson's Degrees

PhD Computer Science Stanford University
Masters Computer Science University of California, Berkeley
Bachelors Computer Science University of California, Berkeley

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Peter A. Clarkson'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

Solitons, Nonlinear Evolution Equations and Inverse Scattering (1992) (4712)
Solitons, Nonlinear Evolution Equations and Inverse Scattering: References (1991) (1120)
New similarity reductions of the Boussinesq equation (1989) (901)
THE DIRECT METHOD IN SOLITON THEORY (Cambridge Tracts in Mathematics 155) (2006) (414)
Symmetry reductions and exact solutions of a class of nonlinear heat equations (1993) (291)
The nonclassical method is more general than the direct method for symmetry reductions. An example of the Fitzhugh-Nagumo equation (1992) (214)
Nonclassical symmetry reductions of the Boussinesq equation (1995) (179)
Painlevé equations: nonlinear special functions (2003) (176)
Painleve analysis of the non-linear Schrodinger family of equations (1987) (152)
Solitary‐Wave Interactions in Elastic Rods (1986) (140)
Algorithms for the Nonclassical Method of Symmetry Reductions (1994) (133)
Rogue waves, rational solutions, the patterns of their zeros and integral relations (2010) (132)
New similarity solutions for the modified Boussinesq equation (1989) (130)
Symmetry and the Chazy Equation (1996) (128)
Bäcklund Transformations and Solution Hierarchies for the Third Painlevé Equation (1995) (125)
Applications of analytic and geometric methods to nonlinear differential equations (1993) (125)
Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach (1998) (120)
The Painlevé‐Kowalevski and Poly‐Painlevé Tests for Integrability (1992) (112)
PAINLEVÉ DIFFERENTIAL EQUATIONS IN THE COMPLEX PLANE (de Gruyter Studies in Mathematics 28) (2003) (110)
On a Shallow Water Wave Equation (1994) (98)
Symmetry Methods for Differential Equations (2016) (93)
Hodograph transformations of linearizable partial differential equations (1989) (91)
New similarity reductions and Painleve analysis for the symmetric regularised long wave and modified Benjamin-Bona-Mahoney equations (1989) (88)
The second Painlevé equation, its hierarchy and associated special polynomials (2003) (88)
Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation (1991) (82)
Painlevé transcendents (2010) (80)
Exact solutions of the multidimensional derivative nonlinear Schrodinger equation for many-body systems of criticality (1990) (79)
The fourth Painlevé equation and associated special polynomials (2003) (72)
Vortices and Polynomials (2008) (71)
Solitons, Nonlinear Evolution Equations and Inverse Scattering: Remarks on Riemann-Hilbert problems (1991) (71)
Rational solutions of the Boussinesq equation and applications to rogue waves (2016) (69)
Rational solutions of a differential-difference KdV equation, the Toda equation and the discrete KdV equation (1995) (65)
Multicomponent equations associated to non-isospectral scattering problems (1997) (63)
Painlevé analysis of the damped, driven nonlinear Schrödinger equation (1988) (63)
Dimensional reductions and exact solutions of a generalized nonlinear Schrodinger equation (1992) (62)
New exact solutions of the Boussinesq equation (1990) (61)
Painlevé Analysis and the Complete Integrability of a Generalized Variable-Coefficient Kadomtsev-Petviashvili Equation (1990) (61)
New similarity solutions of the unsteady incompressible boundary-layer equations (2000) (60)
A connection formula for the second Painlevé transcendent (1988) (53)
The Relationship Between Semiclassical Laguerre Polynomials and the Fourth Painlevé Equation (2013) (51)
Application of Uniform Asymptotics to the Second Painlevé Transcendent (1996) (50)
Similarity Reductions and Exact Solutions for the Two‐Dimensional Incompressible Navier–Stokes Equations (1999) (50)
Symmetries of a class of nonlinear third-order partial differential equations (1996) (50)
The third Painlevé equation and associated special polynomials (2003) (42)
Symmetries and exact solutions of a (2+1)-dimensional sine-Gordon system (1994) (41)
The Painlevé property and a partial differential equation with an essential singularity (1985) (40)
Applications of the Differential Algebra Package diffgrob2 to Classical Symmetries of Differential Equations (1997) (40)
Special Polynomials Associated with Rational Solutions of the Painlevé Equations and Applications to Soliton Equations (2006) (39)
THE LAX PAIR FOR THE MKDV HIERARCHY (2006) (38)
Symmetry Reduction and Exact Solutions of Nonlinear Partial Differential Equations (1999) (37)
Integral equations and exact solutions for the fourth Painlevé equation (1992) (36)
Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations (1998) (34)
Nonclassical symmetry reductions and exact solutions of the Zabolotskaya–Khokhlov equation (1992) (32)
Symmetry group analysis of the shallow water and semi-geostrophic equations (2005) (32)
A Generalized Freud Weight (2015) (31)
The Symmetric Fourth Painlevé Hierarchy and Associated Special Polynomials (2008) (30)
Numerical studies of the fourth Painlevé equation (1993) (29)
Special polynomials associated with rational solutions of the defocusing nonlinear Schrödinger equation and the fourth Painlevé equation (2006) (29)
Nonclassical Reductions of a 3+1-Cubic Nonlinear Schrodinger System (1998) (29)
Symmetries and exact solutions for a 2 + 1-dimensional shallow water wave equation (1997) (29)
Special polynomials associated with rational solutions of the fifth Painlevé equation (2005) (28)
Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations (2013) (27)
PAINLEVÉ EQUATIONS THROUGH SYMMETRY (Translations of Mathematical Monographs 223) (2006) (26)
Integrability of Klein Gordon equations (1986) (25)
Rational Solutions Of The Boussinesq Equation (2008) (25)
Nonclassical symmetry reductions of nonlinear partial differential equations (1993) (25)
Properties of generalized Freud polynomials (2016) (25)
New symmetry reductions and exact solutions of the Davey–Stewartson system. I. Reductions to ordinary differential equations (1994) (24)
SZEGŐ POLYNOMIALS FROM HYPERGEOMETRIC FUNCTIONS (2010) (24)
Remarks on the Yablonskii–Vorob'ev polynomials (2003) (24)
From nonlinearity to coherence : universal features of nonlinear behaviour in many-body physics (1997) (23)
The classical, direct, and nonclassical methods for symmetry reductions of nonlinear partial differential equations (1997) (23)
The Painleve´ property, a modified Boussinesq equation and a modified Kadomtsev-Petviashvili equation (1986) (20)
On Airy Solutions of the Second Painlevé Equation (2015) (19)
Darboux transformations and the symmetric fourth Painlevé equation (2005) (19)
Symmetry Reductions, Exact Solutions, and Painlevé Analysis for a Generalized Boussinesq Equation (1994) (19)
New integrable differential-difference systems (1997) (18)
Integral Equations and Connection Formulae for the Painlevé Equations (1992) (18)
Painlevé Analysis and Similarity Reductions for the Magma Equation (2006) (18)
BRIAN J. CANTWELL: 612 pp., £95.00 (US$130.00)/£35.95 (US$50.00)(P), ISBN 0-521-77183-8/0-521-77740-2(P) (Cambridge University Press, 2002) (2004) (17)
Open Problems for Painlevé Equations (2019) (17)
On rational solutions of the fourth Painleve equation and its Hamiltonian (2003) (16)
Conservation Laws and Integral Relations for the Boussinesq Equation (2016) (16)
New exact solutions of the discrete fourth Painleve´equation (1994) (15)
The Painlevé conjecture, the Painlevé property for partial differential equations and complete integrability (1986) (13)
Unique positive solution for an alternative discrete Painlevé I equation (2015) (13)
On the relation between the continuous and discrete Painlevé equations (2000) (13)
Ermakov-Painlevé II Reduction in Cold Plasma Physics. Application of a Bäcklund Transformation (2018) (12)
On the application of solutions of the fourth Painlevé equation to various physically motivated nonlinear partial differential equations (1996) (12)
On the Lax Pairs of the Symmetric Painlevé Equations (2006) (12)
Application of the isomonodromy deformation method to the fourth Painlevé equation (1997) (12)
Rational solutions of the classical Boussinesq system (2009) (12)
Cyclic Maya diagrams and rational solutions of higher order Painlevé systems (2018) (12)
Symmetry reductions of a generalized, cylindrical nonlinear Schrodinger equation (1993) (12)
Open Problems in Symmetry Analysis (2001) (12)
Hierarchies of Difference Equations and Bäcklund Transformations (2003) (11)
A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane. (2017) (11)
Symmetries of a Class of Nonlinear Fourth Order Partial Differential Equations (1999) (11)
Solitons, Nonlinear Evolution Equations and Inverse Scattering: Introduction (1991) (11)
Asymptotics of the second Painleve equation (2008) (11)
Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System (2017) (11)
Remarks on the two-dimensional sine-Gordon equation and the Painlevé tests (1985) (10)
Nonclassical Symmetry Reductions and Exact Solutions of Nonlinear Reaction-Diffusion Equations (1993) (10)
Rational solutions of higher order Painlev\'{e} systems I (2018) (9)
On asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert method (1999) (8)
Shallow Water Wave Systems (1998) (8)
The symmetry reductions of a turbulence model (2001) (7)
A generalized sextic Freud weight (2020) (7)
Bäcklund transformations and nonlinear superposition formulae of a differential-difference KdV equation (1998) (6)
Rational Solutions and Bäcklund Transformations for the Third Painlevé Equation (1993) (6)
On integrable Ermakov–Painlevé IV systems (2017) (6)
Solitons and symmetries (1999) (6)
Rational Solutions of an Extended Lotka-Volterra Equation (2002) (5)
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) - Special Issue on Orthogonal Polynomials, Special Functions and Applications (2018) (4)
Hierarchies of exact solutions for the discrete third Painlevé equation (2000) (4)
Applications of the Dierential Algebra Package diffgrob2 to Classical Symmetries of Dierential Equations (1997) (3)
Inverse Scattering for the Korteweg-de Vries Equation (1991) (3)
Backlund Transformations and Hierarchies of Exact Solutions for the Fourth Painleve Equation and their Application to Discrete Equations (1994) (3)
SPECIAL POLYNOMIALS ASSOCIATED WITH RATIONAL AND ALGEBRAIC SOLUTIONS OF THE PAINLEV´ E EQUATIONS (2006) (3)
Generalised Airy polynomials (2020) (3)
One hundred years of PVI, the Fuchs–Painlevé equation (2006) (3)
The fourth Painleve equation (2008) (3)
Discrete equations and the singular manifold method (1999) (3)
Symmetries of the Nonlinear Heat Equation (1993) (3)
Symmetry, the Chazy equation and Chazy hierarchies (2002) (2)
An algebraic proof for the Umemura polynomials for the third Painlevé equation (2016) (2)
Symmetry Reductions and Exact Solutions for a Generalised Boussinesq Equation (1993) (2)
Special Polynomials and Exact Solutions of the Dispersive Water Wave and Modified Boussinesq Equations (2009) (2)
Nonclassical Symmetry Reductions of a Generalized Nonlinear Schrödinger Equation (1991) (2)
General Inverse Scattering in One Dimension (1991) (2)
Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14) (2018) (2)
A STUDY OF THE FOURTH PAINLEVE EQUATION (1993) (2)
An constructive proof for the Umemura polynomials for the third Painlev\'e equation. (2016) (2)
On Discrete Painlev´ e equations as B¨ acklund Transformations (2000) (1)
R-matrix hierarchies, integrable lattice systems and their integrable discretizations (1999) (1)
Classical solutions of the degenerate fifth Painlevé equation (2023) (1)
Erratum: Reductions of self-dual Yang-Mills fields and classical systems [Phys. Rev. Lett. 65, 1085 (1990)] (1990) (1)
On Discrete Painleve Equations as Backlund Transformations (2002) (1)
Solitons, Nonlinear Evolution Equations and Inverse Scattering: Remarks on ∂ problems (1991) (0)
Symmetries and Integrability of Difference Equations: Preface (1999) (0)
Symmetries and Integrability of Difference Equations: Generalized Bäcklund transformation and new explicit solutions of the two-dimensional Toda equation (1999) (0)
Examples of Nonclassical Similarity Reductions (1990) (0)
The Painlevé tests and complete integrability (1987) (0)
Preface: Orthogonal polynomials, special functions, and applications (2018) (0)
Special Issue: Orthogonal Polynomials, Special Functions and Applications (2018) (0)
Symmetry Reductions and Exact Solutions of the Davey-Stewartson System (1993) (0)
Inverse Scattering in Two Dimensions (1991) (0)
Inverse Scattering in Multidimensions (1991) (0)
Rational Solutions of the Fifth Painlev\'e Equation. Generalised Laguerre Polynomials (2023) (0)
Solitons, Nonlinear Evolution Equations and Inverse Scattering: The Painlevé Equations (1991) (0)
On a ShallowWaterWave Equation (1993) (0)
Book Review (2001) (0)
C A ] 28 O ct 2 01 5 A Generalized Freud Weight (2015) (0)
Problems for Painlevé Equations (2019) (0)
Problems in Symmetry Analysis (2009) (0)
Symmetries and Integrability of Difference Equations: Discrete Geometry (1999) (0)
Further Remarks and Open Problems (1991) (0)
The Relationship Between Semiclassical Laguerre Polynomials and the Fourth Painlevé Equation (2013) (0)
Generalized higher-order Freud weights (2022) (0)
A note on solutions of Painlevé II (1982) (0)
New Similarity Reductions of Boussinesq-Type Equations (1990) (0)
Solitons, Nonlinear Evolution Equations and Inverse Scattering: Inverse Scattering for Integro-Differential Equations (1991) (0)
Painlevé Equations and Associated Polynomials (2005) (0)
Special issue: One hundred years of PVI, the Fuchs–Painlevé equation (2005) (0)
A.P. Magnus, Freud’s equations for orthogonal polynomials as discrete Painlevé equations, pp. 228-243 in Symmetries and Integrability of Difference (0)

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Peter A. Clarkson's AcademicInfluence.com Rankings