Boris Dubrovin
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Russian mathematician
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Boris Dubrovin mathematics Degrees
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Algebraic Geometry
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Geometry
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Mathematics
Why Is Boris Dubrovin Influential?
(Suggest an Edit or Addition)According to Wikipedia, Boris Anatolievich Dubrovin was a Russian mathematician, Doctor of Physical and Mathematical Sciences . After his death, the Dubrovin Medal was created in his memory, and is awarded to promising researchers who make outstanding contributions to the fields of mathematical physics and geometry.
Boris Dubrovin '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
- Geometry of 2D topological field theories (1994) (1381)
- Modern geometry--methods and applications (1984) (1154)
- Theta functions and non-linear equations (1981) (693)
- NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES (1976) (656)
- Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory (1989) (475)
- Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants (2001) (331)
- Integrable systems in topological field theory (1992) (329)
- The geometry of surfaces, transformation groups, and fields (1984) (251)
- The Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogoliubov-Whitham averaging method (1983) (230)
- Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation (1997) (215)
- Monodromy of certain Painlevé–VI transcendents and reflection groups (1998) (210)
- ON POISSON BRACKETS OF HYDRODYNAMIC TYPE (2008) (199)
- Periodic problems for the Korteweg — de Vries equation in the class of finite band potentials (1975) (194)
- Modern Geometry-Methods and Applications(Part II. The Geometry and Topology of Manifolds) (2010) (182)
- Geometry and integrability of topological-antitopological fusion (1992) (171)
- Geometry and analytic theory of Frobenius manifolds (1998) (162)
- Painleve transcendents in two-dimensional topological eld theory (1999) (157)
- On Hamiltonian Perturbations of Hyperbolic Systems of Conservation Laws, II: Universality of Critical Behaviour (2005) (147)
- The Extended Toda Hierarchy (2003) (145)
- On Hamiltonian perturbations of hyperbolic systems of conservation laws I: Quasi‐Triviality of bi‐Hamiltonian perturbations (2004) (137)
- ON ALMOST DUALITY FOR FROBENIUS MANIFOLDS (2003) (137)
- Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginsburg models (1992) (132)
- Frobenius manifolds and Virasoro constraints (1998) (125)
- Integrable Systems. I (2001) (115)
- On Universality of Critical Behavior in the Focusing Nonlinear Schrödinger Equation, Elliptic Umbilic Catastrophe and the Tritronquée Solution to the Painlevé-I Equation (2009) (115)
- PERIODIC AND CONDITIONALLY PERIODIC ANALOGS OF THE MANY-SOLITON SOLUTIONS OF THE KORTEWEG-DE VRIES EQUATION (1974) (113)
- Extended affine Weyl groups and Frobenius manifolds (1996) (111)
- Differential geometry of the space of orbits of a Coxeter group (1993) (110)
- Flat pencils of metrics and Frobenius manifolds (1998) (110)
- Inverse problem for periodic finite — zoned potentials in the theory of scattering (1975) (108)
- Completely integrable Hamiltonian systems associated with matrix operators and Abelian varieties (1977) (106)
- Virasoro Symmetries of the Extended Toda Hierarchy (2003) (102)
- Real two-zone solutions of the sine-Gordon equation (1982) (83)
- Matrix finite-zone operators (1985) (79)
- REAL THETA-FUNCTION SOLUTIONS OF THE KADOMTSEV–PETVIASHVILI EQUATION (1989) (78)
- Hamiltonian formalism of one-dimensional systems of hydrodynamic type (1983) (76)
- THE SCHRÖDINGER EQUATION IN A PERIODIC FIELD AND RIEMANN SURFACES (2007) (70)
- Integrable Systems and Classification of 2-Dimensional Topological Field Theories (1993) (69)
- Canonical Structure and Symmetries of the Schlesinger Equations (2003) (67)
- Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures (2007) (62)
- On universality of critical behaviour in Hamiltonian PDEs (2008) (58)
- Correlation functions of the KdV hierarchy and applications to intersection numbers over M¯g,n (2015) (57)
- Integrable Systems and Quantum Groups (1996) (50)
- Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs (2014) (49)
- Géométrie contemporaine : méthodes et applications (1982) (47)
- METHODS OF ALGEBRAIC GEOMETRY IN THE THEORY OF NON-LINEAR EQUATIONS (2017) (46)
- Hydrodynamics of soliton lattices (1993) (38)
- Simple Lie algebras and topological ODEs (2015) (35)
- The geometry and topology of manifolds (1985) (34)
- Minimal Liouville gravity correlation numbers from Douglas string equation (2013) (34)
- Three‐Phase Solutions of the Kadomtsev–Petviashvili Equation (1997) (32)
- MAGNETIC BLOCH FUNCTIONS AND VECTOR BUNDLES. TYPICAL DISPERSION LAWS AND THEIR QUANTUM NUMBERS (2007) (32)
- Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems (2009) (32)
- Generating series for GUE correlators (2016) (32)
- Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory (1991) (32)
- Classical Hurwitz numbers and related combinatorics (2016) (31)
- Tau-Structure for the Double Ramification Hierarchies (2016) (30)
- Monodromy of certain Painlev e-VI transcendents and reection groups (2006) (29)
- Numerical Study of Breakup in Generalized Korteweg-de Vries and Kawahara Equations (2010) (28)
- Differential geometry of strongly integrable systems of hydrodynamic type (1990) (28)
- Poisson brackets on presymplectic manifolds (1993) (27)
- Isomonodromy deformations at an irregular singularity with coalescing eigenvalues (2017) (27)
- On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations (2013) (27)
- Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions (2009) (27)
- Painleve' transcendents and two-dimensional topological field theory (1998) (26)
- On the critical behavior in nonlinear evolutionary PDEs with small viscosity (2012) (25)
- Alternative Hamiltonian Description for Quantum Systems (1990) (25)
- Extended affine Weyl groups of BCD-type: Their Frobenius manifolds and Landau–Ginzburg superpotentials (2019) (24)
- Hamiltonian PDEs: deformations, integrability, solutions (2010) (24)
- Integrable Systems of Double Ramification Type (2016) (22)
- Helix Structures in Quantum Cohomology of Fano Varieties (2018) (21)
- Hodge–GUE Correspondence and the Discrete KdV Equation (2016) (21)
- On tau-functions for the KdV hierarchy (2018) (20)
- Gromov–Witten invariants of the Riemann sphere (2018) (20)
- THE TOPOLOGICAL PROOF OF ABEL–RUFFINI THEOREM (2007) (20)
- Gromov - Witten invariants and integrable hierarchies of topological type (2013) (19)
- Exact solutions of the time-dependent Schroedinger equation with self-consistent potential (1988) (18)
- Simple Lie Algebras, Drinfeld–Sokolov Hierarchies, and Multi-Point Correlation Functions (2016) (17)
- On cubic Hodge integrals and random matrices (2016) (17)
- Local Moduli of Semisimple Frobenius Coalescent Structures (2017) (17)
- Integrable functional equations and algebraic geometry (1994) (17)
- Algebraic-geometrical Darboux coordinates in R-matrix formalism (1994) (17)
- Theory of operators and real algebraic geometry (1988) (16)
- THE KADOMCEV-PETVIAŠVILI EQUATION AND THE RELATIONS BETWEEN THE PERIODS OF HOLOMORPHIC DIFFERENTIALS ON RIEMANN SURFACES (1982) (16)
- Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials (2015) (15)
- On Gromov – Witten invariants of P 1 (2019) (14)
- On critical behaviour in generalized Kadomtsev-Petviashvili equations (2015) (14)
- On universality of critical behaviour in the focusing nonlinear Schr\"odinger equation, elliptic umbilic catastrophe and the {\it tritronqu\'ee} solution to the Painlev\'e-I equation (2007) (14)
- Separation of variables for linear Lax algebras and classical r-matrices (2018) (14)
- Symplectic Field Theory of a Disk, Quantum Integrable Systems, and Schur Polynomials (2014) (14)
- Bihamiltonian Cohomologies and Integrable Hierarchies II: The Tau Structures (2017) (12)
- The averaging of non-local Hamiltonian structures in Whitham ’ s method (2002) (11)
- Functionals of the Peierls - Fröhlich Type and the Variational Principle for the Whitham Equations (1997) (11)
- Topological Conformal Field Theory from the Point of View of Integrable Systems (1993) (10)
- On the reductions and classical solutions of the Schlesinger equations (2006) (10)
- Geometry of Hamiltonian Evolutionary Systems (1991) (10)
- Matrix Resolvent and the Discrete KdV Hierarchy (2019) (9)
- A Riemann-Hilbert Approach to the Heun Equation (2018) (9)
- On an isomonodromy deformation equation without the Painlevé property (2013) (9)
- Differential-geometric Poisson brackets on a lattice (1989) (8)
- The Theory of Surfaces (1984) (8)
- Geometry in Regions of a Space. Basic Concepts (1984) (8)
- Remarks on intersection numbers and integrable hierarchies, I: Quasi-triviality (2019) (8)
- On Gromov–Witten invariants of $\mathbb{P}^1$ (2017) (8)
- On the genus two free energies for semisimple Frobenius manifolds (2012) (7)
- Differential geometry of moduli spaces (1998) (6)
- WDVV Equations and Frobenius Manifolds (2006) (6)
- Topological and Algebraic Geometry Methods in Contemporary Mathematical Physics (2004) (6)
- Integrable systems and classification of 2D topological field theories (1993) (6)
- Extended affine Weyl groups and Frobenius manifolds -- II (2005) (6)
- Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality (2021) (5)
- Hamiltonian partial differential equations and Frobenius manifolds (2008) (5)
- Hamiltonian PDEs and Frobenius manifolds (2008) (5)
- Symplectic Field Theory of a Disk, Quantum Integrable Systems, and Schur Polynomials (2015) (4)
- Algebraic Spectral Curves over Q and their Tau-Functions (2020) (4)
- Functionals of the Peierls - Frhlich type and variational principle for Whitham equations (1996) (4)
- Bihamiltonian structures of PDEs and Frobenius manifolds (2005) (4)
- Topology, Geometry, Integrable Systems, and Mathematical Physics (2014) (3)
- Classical double, R-operators, and negative flows of integrable hierarchies (2010) (3)
- Hamiltonian Formalism for One-Dimensional Systems of Hydrodynamic Type and the Bogolyubov-Whitman Averaging Method - Sov. Math. Dokl. 27, 665 (1983) (1996) (2)
- On a class of compact perturbations of the special pole-free joint solution of KdV and $P_I^2.$ (2019) (2)
- Recurrent procedure for the determination of the Free Energy $\epsilon^{2}$-expansion in the Topological String Theory (1999) (2)
- Examples of Manifolds (1985) (2)
- Separation of variables for quadratic algebras and skew-symmetric classical r-matrices (2019) (2)
- Conference on Riemann-Hilbert Problems, Integrability and Asymptotics (2005) (2)
- Generalized Witt groups (1973) (2)
- International Workshop Analytic and geometric theory of the Camassa-Holm equation and integrable systems (Bologna, 22-25 September 2004). (2004) (1)
- Homology and Cohomology. Computational Recipes (1990) (1)
- Dispersion Relations for Nonlinear Waves and the Schottky Problem (1993) (1)
- Tensors: The Algebraic Theory (1984) (1)
- Part III : Applications of Differential Geometry to Physics (2011) (1)
- Aspects of p-adic geometry related to entanglement entropy (2020) (1)
- Symmetries and casimir of an extended classical long wave system (2013) (1)
- The Elements of the Calculus of Variations (1984) (1)
- Approximating tau-functions by theta-functions (2018) (1)
- Critical Points of Smooth Functions and Homology Theory (1990) (1)
- On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations (2015) (1)
- On analytic families of invariant tori for PDEs (2004) (1)
- Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method (2021) (1)
- Weakly deformed soliton lattices (1990) (1)
- Spectral Theory of Linear λ-Matrices and the Solution of Certain Nonlinear Algebraic and Functional Equations (1993) (1)
- Minimal Liouville gravity correlation numbers from Douglas string equation (2014) (0)
- Foundational Questions. Essential Facts Concerning Functions on a Manifold. Typical Smooth Mappings (1985) (0)
- On an isomonodromy deformation equation without the Painlevé property (2014) (0)
- On Gromov–Witten invariants of P (2018) (0)
- Classical double, R-operators, and negative flows of integrable hierarchies (2012) (0)
- Geometria contemporanea : metodi e applicazioni (1999) (0)
- Symmetries and casimir of an extended classical long wave system (2013) (0)
- Viktor Matveevich Buchstaber (on his 70th birthday) (2013) (0)
- I. M. Krichever Methods of algebraic geometry in the theory of non-linear equations (2018) (0)
- Matrix Resolvent and the Discrete KdV Hierarchy (2020) (0)
- Algebraic spectral curves over $\mathbb Q$ and their tau-functions. (2018) (0)
- Perturbative techniques for integrable systems (2009) (0)
- Smooth Fibre Bundles (1985) (0)
- ASYMPTOTIC BEHAVIOUR OF THE RESOLVENT OF STURM-LIOUVILLE EQUATIONS AND THE ALGEBRA OF THE KORTEWEG-DE VRIES EQUATIONS (2017) (0)
- The Degree of a Mapping. The Intersection Index of Submanifolds. Applications (1985) (0)
- Orientability of Manifolds. The Fundamental Group. Covering Spaces (Fibre Bundles with Discrete Fibre) (1985) (0)
- Bihamiltonian Cohomologies and Integrable Hierarchies II: The Tau Structures (2018) (0)
- main problem remained finding effective conditions for the reality of the "finite-zone" solutions constructed. This problem is completely solved in the present paper.* (1982) (0)
- Singularity Theory and Integrable Systems Organised (2013) (0)
- The Differential Calculus of Tensors (1984) (0)
- INTEGRABILITY IN ALGEBRA, GEOMETRY AND PHYSICS: NEW TRENDS (2015) (0)
- O ct 2 01 5 Simple Lie algebras and topological ODEs (2018) (0)
- Vladimir Petrovich Platonov (on his fiftieth birthday) (1990) (0)
- Cobordisms and Smooth Structures (1990) (0)
- Integrable Systems: Non-linear equations of Korteweg-de Vries type, finite-zone linear operators and abelian varieties (Volume 31, 1976) (1981) (0)
- Bi-Hamiltonian Systems and All That Conference in honour of Franco Magri's 65th birthday Talks and Abstracts S. Benenti: Recent results on non-holonomic dynamical systems (2011) (0)
- Flat Structure on the Space of Isomonodromic Deformations (2020) (0)
- On the critical behavior in nonlinear evolutionary PDEs with small viscosity (2012) (0)
- Александр Петрович Веселов (к 60-летию со дня рождения)@@@Aleksandr Petrovich Veselov (on his 60th birthday) (2016) (0)
- Some Examples of Dynamical Systems and Foliations on Manifolds (1985) (0)
- APPLICATION OF GENERALIZED ANALYTIC FUNCTIONS ON RIEMANN SURFACES TO THE INVESTIGATION OF -DEFORMATIONS OF TWO-DIMENSIONAL SURFACES IN (2017) (0)
- Sergei Petrovich Novikov (on his fiftieth birthday) (1988) (0)
- On tau-functions for the KdV hierarchy (2021) (0)
- Introduction to homology theory (1990) (0)
- The Calculus of Variations in Several Dimensions. Fields and Their Geometric Invariants (1984) (0)
- D ec 2 01 8 TAU-STRUCTURE FOR THE DOUBLE RAMIFICATION HIERARCHIES (2018) (0)
- The Global Structure of Solutions of Higher-Dimensional Variational Problems (1985) (0)
- ALGEBRO-GEOMETRIC POISSON BRACKETS FOR REAL FINITE-ZONE SOLUTIONS OF THE SINE-GORDON EQUATION AND THE NONLINEAR SCHRÖDINGER EQUATION (2007) (0)
- Singularity Theory and Integrable Systems (2012) (0)
- The classification of nonsingular multidimensional (0)
- On the genus two free energies for semisimple Frobenius manifolds (2012) (0)
- PRYM VARIETIES OF BRANCHED COVERINGS AND NONLINEAR EQUATIONS (2016) (0)
- Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations (2011) (0)
- Tau-Structure for the Double Ramification Hierarchies (2018) (0)
- INVERSE P ROBLEM F OR P ERIODIC F INITE-ZONED POTENTIALS I N T HE T HEORY O F S CATTERING (1975) (0)
- Quantum Cohomology: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 30 - July 8, 1997 (2002) (0)
- Generating series for GUE correlators (2017) (0)
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Boris Dubrovin is affiliated with the following schools:
