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Dubrovin, Boris Anatol’evich

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Author ID: dubrovin.boris-a Recent zbMATH articles by "Dubrovin, Boris Anatol'evich"
Published as: Dubrovin, B.; Dubrovin, B. A.; Dubrovin, Boris; Dubrovin, Boris A.
Homepage: http://people.sissa.it/~dubrovin/
External Links: MGP · Math-Net.Ru · Wikidata · ORCID · dblp · GND
Documents Indexed: 120 Publications since 1973, including 15 Books
Biographic References: 2 Publications
all top 5

Serials

10 Communications in Mathematical Physics
8 Soviet Mathematics. Doklady
7 Functional Analysis and its Applications
6 Russian Mathematical Surveys
4 Graduate Texts in Mathematics
3 Soviet Scientific Reviews. Section C
3 Uspekhi Matematicheskikh Nauk [N. S.]
3 Advances in Mathematics
3 Russian Journal of Mathematical Physics
2 Journal of Mathematical Physics
2 Duke Mathematical Journal
2 Funktsional’nyĭ Analiz i ego Prilozheniya
2 Mathematics of the USSR. Izvestiya
2 Physica D
2 Journal of Nonlinear Science
2 Moscow Mathematical Journal
2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
2 Communications in Number Theory and Physics
1 Modern Physics Letters A
1 International Journal of Modern Physics A
1 Communications on Pure and Applied Mathematics
1 Letters in Mathematical Physics
1 Mathematical Notes
1 Matematicheskie Zametki
1 Theoretical and Mathematical Physics
1 Compositio Mathematica
1 Inventiones Mathematicae
1 Journal of Soviet Mathematics
1 Mathematische Annalen
1 Studies in Applied Mathematics
1 IMRN. International Mathematics Research Notices
1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
1 SIAM Journal on Applied Mathematics
1 Nuclear Physics, B, Proceedings Supplements
1 Selecta Mathematica. New Series
1 Mathematical Research Letters
1 Documenta Mathematica
1 Journal of High Energy Physics
1 Annales Henri Poincaré
1 Oberwolfach Reports
1 Pure and Applied Mathematics Quarterly
1 Lecture Notes in Mathematics
1 Classic Reviews in Mathematics and Mathematical Physics
1 Journal of Physics A: Mathematical and Theoretical
1 Translations. Series 2. American Mathematical Society

Publications by Year

Citations contained in zbMATH

102 Publications have been cited 2,595 times in 1,753 Documents Cited by Year
Geometry of 2D topological field theories. Zbl 0841.58065
Dubrovin, Boris
272
1996
Theta functions and non-linear equations. Zbl 0549.58038
Dubrovin, B. A.
156
1981
Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory. Zbl 0712.58032
Dubrovin, B. A.; Novikov, S. P.
139
1989
Nonlinear equations of Korteweg-de Vries type, finite-band linear operators and abelian varieties. Zbl 0326.35011
Dubrovin, B. A.; Matveev, V. B.; Novikov, S. P.
115
1976
Non-linear equations of Korteweg-deVries type, finite-zone linear operators, and Abelian varieties. Zbl 0346.35025
Dubrovin, B. A.; Matveev, V. B.; Novikov, S. P.
114
1976
Theta-functions and non-linear equations. Zbl 0478.58038
Dubrovin, B. A.
87
1981
Hamiltonian formalism of one-dimensional systems of hydrodynamic type, and the Bogolyubov-Whitman averaging method. Zbl 0553.35011
Dubrovin, B. A.; Novikov, S. P.
83
1983
Modern geometry - methods and applications. Part I: The geometry of surfaces, transformation groups, and fields. Transl. from the Russian by Robert G. Burns. Zbl 0529.53002
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
74
1984
Modern geometry - methods and applications. Part I. The geometry of surfaces, transformation groups, and fields. Transl. by Robert G. Burns. 2nd ed. Zbl 0751.53001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
72
1992
Modern geometry - methods and applications. Part 2: The geometry and topology of manifolds. Transl. from the Russian by Robert G. Burns. Zbl 0565.57001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
69
1985
On Poisson brackets of hydrodynamic type. Zbl 0591.58012
Dubrovin, B. A.; Novikov, S. P.
69
1984
Monodromy of certain Painlevé-VI transcendents and reflection groups. Zbl 0960.34075
Dubrovin, B.; Mazzocco, M.
54
2000
Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation. Zbl 0923.58060
Dubrovin, Boris; Zhang, Youjin
51
1998
Painlevé transcendents in two-dimensional topological field theory. Zbl 1026.34095
Dubrovin, Boris
48
1999
Modern geometry. Methods and applications. Textbook. (Sovremennaya geometriya. Metody i prilozheniya. Uchebnoe posobie). 2nd ed., rev. Zbl 0601.53001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
48
1986
Integrable systems. I. Zbl 0780.58019
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
48
1985
On Hamiltonian perturbations of hyperbolic systems of conservation laws. II: Universality of critical behaviour. Zbl 1109.35070
Dubrovin, Boris
46
2006
Periodic problems for the Korteweg-de Vries equation in the class of finite band potentials. Zbl 0358.35022
Dubrovin, B. A.
46
1976
On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation. Zbl 1220.37048
Dubrovin, B.; Grava, T.; Klein, C.
43
2009
The extended Toda hierarchy. Zbl 1076.37055
Carlet, Guido; Dubrovin, Boris; Zhang, Youjin
43
2004
Geometry and integrability of topological-antitopological fusion. Zbl 0771.53042
Dubrovin, B.
41
1993
The Schrödinger equation in a periodic field and Riemann surfaces. Zbl 0441.35021
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
41
1976
On Hamiltonian perturbations of hyperbolic systems of conservation laws. I: Quasi-triviality of bi-Hamiltonian perturbations. Zbl 1108.35112
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
39
2006
Hamiltonian formalism of Whitham-type hierarchies and topological Landau- Ginsburg models. Zbl 0753.58039
Dubrovin, B. A.
35
1992
Inverse problem for periodic finite-zoned potentials in the theory of scattering. Zbl 0315.35072
Dubrovin, B. A.
34
1975
On almost duality for Frobenius manifolds. Zbl 1063.53092
Dubrovin, Boris
31
2004
Extended affine Weyl groups and Frobenius manifolds. Zbl 0964.32020
Dubrovin, Boris; Zhang, Youjin
31
1998
Modern geometry - methods and applications. Part III. Introduction to homology theory. Transl. from the Russian by Robert G. Burns. Zbl 0703.55001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
31
1990
Geometry and analytic theory of Frobenius manifolds. Zbl 0916.32018
Dubrovin, Boris
30
1998
Frobenius manifolds and Virasoro constraints. Zbl 0963.81066
Dubrovin, Boris; Zhang, Youjin
25
1999
Real two-zone solutions of the sine-Gordon equation. Zbl 0554.35100
Dubrovin, B. A.; Natanzon, S. M.
25
1982
Modern geometry. (Sovremennaya geometriya). Zbl 0433.53001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
25
1980
On universality of critical behaviour in Hamiltonian PDEs. Zbl 1172.35001
Dubrovin, Boris
23
2008
Virasoro symmetries of the extended Toda hierarchy. Zbl 1071.37054
Dubrovin, Boris; Zhang, Youjin
22
2004
Matrix finite-zone operators. Zbl 0561.58043
Dubrovin, B. A.
21
1985
Dynamical systems. IV: Integrable systems. Zbl 0591.58013
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
20
1985
Flat pencils of metrics and Frobenius manifolds. Zbl 0963.53054
Dubrovin, Boris
19
1998
A periodicity problem for the Korteweg- de Vries and Sturm-Liouville equations. Their connection with algebraic geometry. Zbl 0312.35015
Dubrovin, B. A.; Novikov, S. P.
19
1974
Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures. Zbl 1153.37032
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
18
2008
Integrable systems and classification of 2-dimensional topological field theories. Zbl 0824.58029
Dubrovin, B.
18
1993
Completely integrable Hamiltonian systems associated with matrix operators and abelian varieties. Zbl 0413.58012
Dubrovin, B. A.
18
1978
Canonical structure and symmetries of the Schlesinger equations. Zbl 1146.32005
Dubrovin, Boris; Mazzocco, Marta
17
2007
Real theta-function solutions of the Kadomtsev-Petviashvili equation. Zbl 0672.35072
Dubrovin, B. A.; Natanzon, S. M.
16
1988
Differential geometry of the space of orbits of a Coxeter group. Zbl 0962.53049
Dubrovin, Boris
14
1998
Modern geometry. Methods of homology theory. Zbl 0582.55001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
14
1984
Correlation functions of the KdV hierarchy and applications to intersection numbers over \(\overline{\mathcal{M}}_{g, n}\). Zbl 1373.37153
Bertola, Marco; Dubrovin, Boris; Yang, Di
13
2016
Minimal Liouville gravity correlation numbers from Douglas string equation. Zbl 1333.83172
Belavin, Alexander; Dubrovin, Boris; Mukhametzhanov, Baur
13
2014
Numerical study of breakup in generalized Korteweg-de Vries and Kawahara equations. Zbl 1231.65175
Dubrovin, B.; Grava, T.; Klein, C.
13
2011
Infinite-dimensional Frobenius manifolds for \(2+1\) integrable systems. Zbl 1208.53090
Carlet, Guido; Dubrovin, Boris; Mertens, Luca Philippe
13
2011
Ground states in a periodic field. Magnetic Bloch functions and vector bundles. Zbl 0489.46055
Dubrovin, B. A.; Novikov, S. P.
13
1980
On the critical behavior in nonlinear evolutionary PDEs with small viscosity. Zbl 1263.35019
Dubrovin, B.; Elaeva, M.
12
2012
Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. Zbl 1335.53114
Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin
11
2016
Hamiltonian PDEs: deformations, integrability, solutions. Zbl 1221.37112
Dubrovin, B.
11
2010
Ein periodisches Problem für die Korteweg-de Vries-Gleichung in der Klasse der endlich-zonalen Potentiale. Zbl 0338.35022
Dubrovin, B. A.
10
1975
Three-phase solutions of the Kadomtsev-Petviashvili equation. Zbl 0893.35112
Dubrovin, B. A.; Flickinger, Ron; Segur, Harvey
9
1997
Alternative Hamiltonian description for quantum systems. Zbl 1020.81606
Dubrovin, B. A.; Marmo, G.; Simoni, A.
9
1990
Differential geometry of strongly integrable systems of hydrodynamic type. Zbl 0850.76008
Dubrovin, B. A.
9
1990
On critical behaviour in systems of Hamiltonian partial differential equations. Zbl 1321.35208
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio
8
2015
Tau-structure for the double ramification hierarchies. Zbl 1431.53095
Buryak, Alexandr; Dubrovin, Boris; Guéré, Jérémy; Rossi, Paolo
7
2018
Generating series for GUE correlators. Zbl 1380.37126
Dubrovin, Boris; Yang, Di
7
2017
Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions. Zbl 1207.35032
Dubrovin, Boris
7
2009
Poisson brackets on presymplectic manifolds. Zbl 0984.37500
Dubrovin, B. A.; Giordano, M.; Marmo, G.; Simoni, A.
7
1993
Hydrodynamics of soliton lattices. Zbl 0845.58027
Dubrovin, B. A.; Novikov, S. P.
7
1993
Géométrie contemporaine. Méthodes et applications. Deuxième partie: Géométrie et topologie des variates. Traduit du russe par Vladimir Kotliar. Zbl 0502.53003
Dubrovin, B.; Novikov, S.; Fomenko, A.
6
1982
Isomonodromy deformations at an irregular singularity with coalescing eigenvalues. Zbl 1416.34079
Cotti, Giordano; Dubrovin, Boris; Guzzetti, Davide
5
2019
Simple Lie algebras and topological ODEs. Zbl 1406.17016
Bertola, Marco; Dubrovin, Boris; Yang, Di
5
2018
Separation of variables for linear Lax algebras and classical \(r\)-matrices. Zbl 1403.37067
Dubrovin, B.; Skrypnyk, T.
5
2018
On critical behaviour in generalized Kadomtsev-Petviashvili equations. Zbl 1415.37095
Dubrovin, B.; Grava, T.; Klein, C.
5
2016
Gromov-Witten invariants and integrable hierarchies of topological type. Zbl 1370.53060
Dubrovin, B.
5
2014
Algebro-geometric Poisson brackets for real finite-zone solutions of the sine-Gordon equation and the nonlinear Schrödinger equation. Zbl 0574.58015
Dubrovin, B. A.; Novikov, S. P.
5
1982
Topological and algebraic geometry methods in contemporary mathematical physics. II. Zbl 0534.58002
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
5
1982
Classical Hurwitz numbers and related combinatorics. Zbl 1411.14059
Dubrovin, Boris; Yang, Di; Zagier, Don
4
2017
On the genus two free energies for semisimple Frobenius manifolds. Zbl 1325.53114
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
4
2012
On the reductions and classical solutions of the Schlesinger equations. Zbl 1356.32007
Dubrovin, Boris; Mazzocco, Marta
4
2007
Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory. Zbl 0947.35117
Dubrovin, Boris
4
1998
Geometry of Hamiltonian evolutionary systems. Zbl 0936.37022
Dubrovin, Boris A.
4
1991
Géométrie contemporaine. Méthodes et applications. Premiere partie: Géométrie des surfaces, des groupes de transformations et des champs. Traduit du russe par Vladimir Kotliar. Zbl 0502.53002
Dubrovin, B.; Novikov, S.; Fomenko, A.
4
1982
The Kadomtsev-Petviashvili equation and the relations between the periods of holomorphic differentials on Riemann surfaces. Zbl 0501.14016
Dubrovin, B. A.
4
1982
Bihamiltonian cohomologies and integrable hierarchies. II: The tau structures. Zbl 1403.37072
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
3
2018
On cubic Hodge integrals and random matrices. Zbl 1439.14091
Dubrovin, Boris; Yang, Di
3
2017
Symplectic field theory of a disk, quantum integrable systems, and Schur polynomials. Zbl 1342.81626
Dubrovin, Boris
3
2016
On an isomonodromy deformation equation without the Painlevé property. Zbl 1322.34102
Dubrovin, B.; Kapaev, A.
3
2014
Theory of operators and real algebraic geometry. Zbl 0773.35045
Dubrovin, B. A.
3
1987
On Gromov-Witten invariants of \(\mathbb{P}^1\). Zbl 1441.14180
Dubrovin, Boris; Yang, Di
2
2019
Separation of variables for quadratic algebras and skew-symmetric classical \(r\)-matrices. Zbl 1436.70005
Dubrovin, B.; Skrypnyk, T.
2
2019
Extended affine Weyl groups of BCD-type: their Frobenius manifolds and Landau-Ginzburg superpotentials. Zbl 1418.53088
Dubrovin, Boris; Strachan, Ian A. B.; Zhang, Youjin; Zuo, Dafeng
2
2019
Integrable functional equations and algebraic geometry. Zbl 0815.39008
Dubrovin, B. A.; Fokas, A. S.; Santini, P. M.
2
1994
Topological conformal field theory from the point of view of integrable systems. Zbl 0860.58046
Dubrovin, B.
2
1993
Differential-geometric Poisson brackets on a lattice. Zbl 0711.58027
Dubrovin, B. A.
2
1989
Riemann surfaces and nonlinear equations. Textbook. Part 1. Zbl 0692.35079
Dubrovin, B. A.
2
1986
Kadomtsev-Petviashvili equation and relations between the periods of holomorphic differentials on Riemann surfaces. Zbl 0477.14018
Dubrovin, B. A.
2
1981
Generalized Witt groups. Zbl 0274.22004
Dubrovin, B. A.
2
1973
Hodge-GUE correspondence and the discrete KdV equation. Zbl 07258560
Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin
1
2020
Matrix resolvent and the discrete KdV hierarchy. Zbl 07220096
Dubrovin, Boris; Yang, Di
1
2020
Gromov-Witten invariants of the Riemann sphere. Zbl 07167894
Dubrovin, Boris; Yang, Di; Zagier, Don
1
2020
Classical double, \(R\)-operators, and negative flows of integrable hierarchies. Zbl 1341.37035
Dubrovin, B. A.; Skrypnyk, T. V.
1
2012
Hamiltonian PDEs and Frobenius manifolds. Zbl 1170.53072
Dubrovin, B. A.
1
2008
Topological and algebraic geometry methods in contemporary mathematical physics. Zbl 1107.37003
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
1
2004
On analytic families of invariant tori for PDEs. Zbl 1087.35083
Dubrovin, Boris
1
2004
Topology. Methodical instructions. Zbl 0698.54001
Dubrovin, B. A.; Solov’ev, Yu. P.
1
1988
Hodge-GUE correspondence and the discrete KdV equation. Zbl 07258560
Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin
1
2020
Matrix resolvent and the discrete KdV hierarchy. Zbl 07220096
Dubrovin, Boris; Yang, Di
1
2020
Gromov-Witten invariants of the Riemann sphere. Zbl 07167894
Dubrovin, Boris; Yang, Di; Zagier, Don
1
2020
Isomonodromy deformations at an irregular singularity with coalescing eigenvalues. Zbl 1416.34079
Cotti, Giordano; Dubrovin, Boris; Guzzetti, Davide
5
2019
On Gromov-Witten invariants of \(\mathbb{P}^1\). Zbl 1441.14180
Dubrovin, Boris; Yang, Di
2
2019
Separation of variables for quadratic algebras and skew-symmetric classical \(r\)-matrices. Zbl 1436.70005
Dubrovin, B.; Skrypnyk, T.
2
2019
Extended affine Weyl groups of BCD-type: their Frobenius manifolds and Landau-Ginzburg superpotentials. Zbl 1418.53088
Dubrovin, Boris; Strachan, Ian A. B.; Zhang, Youjin; Zuo, Dafeng
2
2019
Tau-structure for the double ramification hierarchies. Zbl 1431.53095
Buryak, Alexandr; Dubrovin, Boris; Guéré, Jérémy; Rossi, Paolo
7
2018
Simple Lie algebras and topological ODEs. Zbl 1406.17016
Bertola, Marco; Dubrovin, Boris; Yang, Di
5
2018
Separation of variables for linear Lax algebras and classical \(r\)-matrices. Zbl 1403.37067
Dubrovin, B.; Skrypnyk, T.
5
2018
Bihamiltonian cohomologies and integrable hierarchies. II: The tau structures. Zbl 1403.37072
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
3
2018
Generating series for GUE correlators. Zbl 1380.37126
Dubrovin, Boris; Yang, Di
7
2017
Classical Hurwitz numbers and related combinatorics. Zbl 1411.14059
Dubrovin, Boris; Yang, Di; Zagier, Don
4
2017
On cubic Hodge integrals and random matrices. Zbl 1439.14091
Dubrovin, Boris; Yang, Di
3
2017
Correlation functions of the KdV hierarchy and applications to intersection numbers over \(\overline{\mathcal{M}}_{g, n}\). Zbl 1373.37153
Bertola, Marco; Dubrovin, Boris; Yang, Di
13
2016
Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. Zbl 1335.53114
Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin
11
2016
On critical behaviour in generalized Kadomtsev-Petviashvili equations. Zbl 1415.37095
Dubrovin, B.; Grava, T.; Klein, C.
5
2016
Symplectic field theory of a disk, quantum integrable systems, and Schur polynomials. Zbl 1342.81626
Dubrovin, Boris
3
2016
On critical behaviour in systems of Hamiltonian partial differential equations. Zbl 1321.35208
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio
8
2015
Minimal Liouville gravity correlation numbers from Douglas string equation. Zbl 1333.83172
Belavin, Alexander; Dubrovin, Boris; Mukhametzhanov, Baur
13
2014
Gromov-Witten invariants and integrable hierarchies of topological type. Zbl 1370.53060
Dubrovin, B.
5
2014
On an isomonodromy deformation equation without the Painlevé property. Zbl 1322.34102
Dubrovin, B.; Kapaev, A.
3
2014
On the critical behavior in nonlinear evolutionary PDEs with small viscosity. Zbl 1263.35019
Dubrovin, B.; Elaeva, M.
12
2012
On the genus two free energies for semisimple Frobenius manifolds. Zbl 1325.53114
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
4
2012
Classical double, \(R\)-operators, and negative flows of integrable hierarchies. Zbl 1341.37035
Dubrovin, B. A.; Skrypnyk, T. V.
1
2012
Numerical study of breakup in generalized Korteweg-de Vries and Kawahara equations. Zbl 1231.65175
Dubrovin, B.; Grava, T.; Klein, C.
13
2011
Infinite-dimensional Frobenius manifolds for \(2+1\) integrable systems. Zbl 1208.53090
Carlet, Guido; Dubrovin, Boris; Mertens, Luca Philippe
13
2011
Hamiltonian PDEs: deformations, integrability, solutions. Zbl 1221.37112
Dubrovin, B.
11
2010
On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation. Zbl 1220.37048
Dubrovin, B.; Grava, T.; Klein, C.
43
2009
Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions. Zbl 1207.35032
Dubrovin, Boris
7
2009
On universality of critical behaviour in Hamiltonian PDEs. Zbl 1172.35001
Dubrovin, Boris
23
2008
Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures. Zbl 1153.37032
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
18
2008
Hamiltonian PDEs and Frobenius manifolds. Zbl 1170.53072
Dubrovin, B. A.
1
2008
Canonical structure and symmetries of the Schlesinger equations. Zbl 1146.32005
Dubrovin, Boris; Mazzocco, Marta
17
2007
On the reductions and classical solutions of the Schlesinger equations. Zbl 1356.32007
Dubrovin, Boris; Mazzocco, Marta
4
2007
On Hamiltonian perturbations of hyperbolic systems of conservation laws. II: Universality of critical behaviour. Zbl 1109.35070
Dubrovin, Boris
46
2006
On Hamiltonian perturbations of hyperbolic systems of conservation laws. I: Quasi-triviality of bi-Hamiltonian perturbations. Zbl 1108.35112
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
39
2006
The extended Toda hierarchy. Zbl 1076.37055
Carlet, Guido; Dubrovin, Boris; Zhang, Youjin
43
2004
On almost duality for Frobenius manifolds. Zbl 1063.53092
Dubrovin, Boris
31
2004
Virasoro symmetries of the extended Toda hierarchy. Zbl 1071.37054
Dubrovin, Boris; Zhang, Youjin
22
2004
Topological and algebraic geometry methods in contemporary mathematical physics. Zbl 1107.37003
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
1
2004
On analytic families of invariant tori for PDEs. Zbl 1087.35083
Dubrovin, Boris
1
2004
Monodromy of certain Painlevé-VI transcendents and reflection groups. Zbl 0960.34075
Dubrovin, B.; Mazzocco, M.
54
2000
Painlevé transcendents in two-dimensional topological field theory. Zbl 1026.34095
Dubrovin, Boris
48
1999
Frobenius manifolds and Virasoro constraints. Zbl 0963.81066
Dubrovin, Boris; Zhang, Youjin
25
1999
Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation. Zbl 0923.58060
Dubrovin, Boris; Zhang, Youjin
51
1998
Extended affine Weyl groups and Frobenius manifolds. Zbl 0964.32020
Dubrovin, Boris; Zhang, Youjin
31
1998
Geometry and analytic theory of Frobenius manifolds. Zbl 0916.32018
Dubrovin, Boris
30
1998
Flat pencils of metrics and Frobenius manifolds. Zbl 0963.53054
Dubrovin, Boris
19
1998
Differential geometry of the space of orbits of a Coxeter group. Zbl 0962.53049
Dubrovin, Boris
14
1998
Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory. Zbl 0947.35117
Dubrovin, Boris
4
1998
Three-phase solutions of the Kadomtsev-Petviashvili equation. Zbl 0893.35112
Dubrovin, B. A.; Flickinger, Ron; Segur, Harvey
9
1997
Geometry of 2D topological field theories. Zbl 0841.58065
Dubrovin, Boris
272
1996
Integrable functional equations and algebraic geometry. Zbl 0815.39008
Dubrovin, B. A.; Fokas, A. S.; Santini, P. M.
2
1994
Geometry and integrability of topological-antitopological fusion. Zbl 0771.53042
Dubrovin, B.
41
1993
Integrable systems and classification of 2-dimensional topological field theories. Zbl 0824.58029
Dubrovin, B.
18
1993
Poisson brackets on presymplectic manifolds. Zbl 0984.37500
Dubrovin, B. A.; Giordano, M.; Marmo, G.; Simoni, A.
7
1993
Hydrodynamics of soliton lattices. Zbl 0845.58027
Dubrovin, B. A.; Novikov, S. P.
7
1993
Topological conformal field theory from the point of view of integrable systems. Zbl 0860.58046
Dubrovin, B.
2
1993
Modern geometry - methods and applications. Part I. The geometry of surfaces, transformation groups, and fields. Transl. by Robert G. Burns. 2nd ed. Zbl 0751.53001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
72
1992
Hamiltonian formalism of Whitham-type hierarchies and topological Landau- Ginsburg models. Zbl 0753.58039
Dubrovin, B. A.
35
1992
Geometry of Hamiltonian evolutionary systems. Zbl 0936.37022
Dubrovin, Boris A.
4
1991
Modern geometry - methods and applications. Part III. Introduction to homology theory. Transl. from the Russian by Robert G. Burns. Zbl 0703.55001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
31
1990
Alternative Hamiltonian description for quantum systems. Zbl 1020.81606
Dubrovin, B. A.; Marmo, G.; Simoni, A.
9
1990
Differential geometry of strongly integrable systems of hydrodynamic type. Zbl 0850.76008
Dubrovin, B. A.
9
1990
Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory. Zbl 0712.58032
Dubrovin, B. A.; Novikov, S. P.
139
1989
Differential-geometric Poisson brackets on a lattice. Zbl 0711.58027
Dubrovin, B. A.
2
1989
Real theta-function solutions of the Kadomtsev-Petviashvili equation. Zbl 0672.35072
Dubrovin, B. A.; Natanzon, S. M.
16
1988
Topology. Methodical instructions. Zbl 0698.54001
Dubrovin, B. A.; Solov’ev, Yu. P.
1
1988
Theory of operators and real algebraic geometry. Zbl 0773.35045
Dubrovin, B. A.
3
1987
Modern geometry. Methods and applications. Textbook. (Sovremennaya geometriya. Metody i prilozheniya. Uchebnoe posobie). 2nd ed., rev. Zbl 0601.53001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
48
1986
Riemann surfaces and nonlinear equations. Textbook. Part 1. Zbl 0692.35079
Dubrovin, B. A.
2
1986
Modern geometry - methods and applications. Part 2: The geometry and topology of manifolds. Transl. from the Russian by Robert G. Burns. Zbl 0565.57001
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
69
1985
Integrable systems. I. Zbl 0780.58019
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
48
1985
Matrix finite-zone operators. Zbl 0561.58043
Dubrovin, B. A.
21
1985
Dynamical systems. IV: Integrable systems. Zbl 0591.58013
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
20
1985
Modern geometry - methods and applications. Part I: The geometry of surfaces, transformation groups, and fields. Transl. from the Russian by Robert G. Burns. Zbl 0529.53002
Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P.
74
1984
On Poisson brackets of hydrodynamic type. Zbl 0591.58012
Dubrovin, B. A.; Novikov, S. P.
69
1984
Modern geometry. Methods of homology theory. Zbl 0582.55001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
14
1984
Hamiltonian formalism of one-dimensional systems of hydrodynamic type, and the Bogolyubov-Whitman averaging method. Zbl 0553.35011
Dubrovin, B. A.; Novikov, S. P.
83
1983
Real two-zone solutions of the sine-Gordon equation. Zbl 0554.35100
Dubrovin, B. A.; Natanzon, S. M.
25
1982
Géométrie contemporaine. Méthodes et applications. Deuxième partie: Géométrie et topologie des variates. Traduit du russe par Vladimir Kotliar. Zbl 0502.53003
Dubrovin, B.; Novikov, S.; Fomenko, A.
6
1982
Algebro-geometric Poisson brackets for real finite-zone solutions of the sine-Gordon equation and the nonlinear Schrödinger equation. Zbl 0574.58015
Dubrovin, B. A.; Novikov, S. P.
5
1982
Topological and algebraic geometry methods in contemporary mathematical physics. II. Zbl 0534.58002
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
5
1982
Géométrie contemporaine. Méthodes et applications. Premiere partie: Géométrie des surfaces, des groupes de transformations et des champs. Traduit du russe par Vladimir Kotliar. Zbl 0502.53002
Dubrovin, B.; Novikov, S.; Fomenko, A.
4
1982
The Kadomtsev-Petviashvili equation and the relations between the periods of holomorphic differentials on Riemann surfaces. Zbl 0501.14016
Dubrovin, B. A.
4
1982
Theta functions and non-linear equations. Zbl 0549.58038
Dubrovin, B. A.
156
1981
Theta-functions and non-linear equations. Zbl 0478.58038
Dubrovin, B. A.
87
1981
Kadomtsev-Petviashvili equation and relations between the periods of holomorphic differentials on Riemann surfaces. Zbl 0477.14018
Dubrovin, B. A.
2
1981
Non-linear equations of Korteweg-de Vries type, finite-zone linear operators, and Abelian varieties. Zbl 0461.35074
Dubrovin, B. A.; Matveev, V. B.; Novikov, S. P.
1
1981
Modern geometry. (Sovremennaya geometriya). Zbl 0433.53001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
25
1980
Ground states in a periodic field. Magnetic Bloch functions and vector bundles. Zbl 0489.46055
Dubrovin, B. A.; Novikov, S. P.
13
1980
On S. P. Novikov’s conjecture in the theory of theta-functions and nonlinear equations of Korteweg-de Vries and Kadomtsev-Petviashvili type. Zbl 0482.35073
Dubrovin, B. A.
1
1980
Completely integrable Hamiltonian systems associated with matrix operators and abelian varieties. Zbl 0413.58012
Dubrovin, B. A.
18
1978
Nonlinear equations of Korteweg-de Vries type, finite-band linear operators and abelian varieties. Zbl 0326.35011
Dubrovin, B. A.; Matveev, V. B.; Novikov, S. P.
115
1976
Non-linear equations of Korteweg-deVries type, finite-zone linear operators, and Abelian varieties. Zbl 0346.35025
Dubrovin, B. A.; Matveev, V. B.; Novikov, S. P.
114
1976
Periodic problems for the Korteweg-de Vries equation in the class of finite band potentials. Zbl 0358.35022
Dubrovin, B. A.
46
1976
The Schrödinger equation in a periodic field and Riemann surfaces. Zbl 0441.35021
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
41
1976
Inverse problem for periodic finite-zoned potentials in the theory of scattering. Zbl 0315.35072
Dubrovin, B. A.
34
1975
Ein periodisches Problem für die Korteweg-de Vries-Gleichung in der Klasse der endlich-zonalen Potentiale. Zbl 0338.35022
Dubrovin, B. A.
10
1975
...and 2 more Documents
all top 5

Cited by 1,706 Authors

35 Dubrovin, Boris Anatol’evich
31 Geng, Xianguo
28 Ferapontov, Evgeny Vladimirovich
25 Zhang, Youjin
21 Pavlov, Maxim V.
21 Strachan, Ian A. B.
19 Klein, Christian
19 Liu, Siqi
18 Grava, Tamara
18 Krichever, Igor’ Moiseevich
17 Grinevich, Pëtr Georgievich
17 Veselov, Alexander Petrovich
16 Mokhov, Oleg I.
15 Gesztesy, Fritz
14 Konopelchenko, Boris Georgievich
14 Lorenzoni, Paolo
14 Novikov, Sergeĭ Petrovich
14 Simon, Barry
12 Dragović, Vladimir
12 Milanov, Todor E.
12 Shadrin, Sergey V.
11 El, Gennady A.
11 He, Guoliang
11 Johnson, Russell Allan
11 Li, Chuanzhong
11 Miller, Peter D.
11 Natanzon, Sergei M.
11 Shamolin, Maksim Vladimirovich
11 Yang, Di
10 Bukhshtaber, Viktor Matveevich
10 Korotkin, Dmitrii A.
10 Marmo, Giuseppe
10 Rossi, Paolo
10 Takasaki, Kanehisa
9 Bertola, Marco
9 Bogoyavlenskij, Oleg Igorevich
9 Carlet, Guido
9 Enolskiĭ, Viktor Zelikovich
9 Fan, Engui
9 Novikov, Roman G.
9 Shabat, Alekseĭ Borisovich
9 Smirnov, Alexander O.
9 Taimanov, Iskander Asanovich
9 Wu, Chaozhong
9 Zeng, Xin
8 Bobenko, Alexander Ivanovich
8 Buryak, Alexandr Y.
8 Falqui, Gregorio
8 Guzzetti, Davide
8 Mironov, Andreĭ Evgen’evich
8 Ortenzi, Giovanni
8 Prykarpatsky, Anatoliy Karolevych
8 Raimondo, Andrea
8 Schäfer, Lars
8 Tu, Minghsien
8 Vitolo, Raffaele F.
8 Wu, Lihua
7 Abenda, Simonetta
7 Agafonov, Sergey I.
7 Belavin, Aleksandr Abramovich
7 Belavin, Vladimir A.
7 Casati, Matteo
7 Chekhov, Leonid O.
7 Chen, Jinbing
7 Dobrokhotov, Sergei Yurievich
7 Harnad, John
7 Iritani, Hiroshi
7 Marshakov, Andrei V.
7 Morozov, Alexei Yurievich
7 Sokolov, Vladimir Vyacheslavovich
7 Stoilov, Nikola M.
7 Xue, Bo
7 Zeng, Yunbo
6 Chalykh, Oleg A.
6 Claeys, Tom
6 David, Liana
6 Deconinck, Bernard
6 Fedorov, Yuri N.
6 Fordy, Allan P.
6 Hertling, Claus
6 Hou, Yu
6 Its, Alexander Rudolfovich
6 Khasanov, Aknazar Bekdurdievich
6 Kuksin, Sergeĭ B.
6 Lee, Niann-Chern
6 Lin, Chang-Shou
6 Lisovyy, Oleg
6 Mal’tsev, Andreĭ Yakovlevich
6 Masoero, Davide
6 Mazzocco, Marta
6 Mironov, Andrei D.
6 Novokshenov, Viktor Yur’evich
6 Odesskii, Alexander
6 Pedroni, Marco
6 Takahashi, Atsushi
6 Tsarev, Sergej Petrovich
6 Zampogni, Luca
6 Zhai, Yunyun
6 Zhang, Hongqing
6 Zuo, Dafeng
...and 1,606 more Authors
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Cited in 255 Serials

130 Communications in Mathematical Physics
114 Journal of Mathematical Physics
113 Journal of Geometry and Physics
90 Theoretical and Mathematical Physics
67 Physica D
59 Letters in Mathematical Physics
57 Functional Analysis and its Applications
47 Advances in Mathematics
36 Journal of Mathematical Sciences (New York)
33 Journal of High Energy Physics
30 Mathematical Notes
29 Journal of Nonlinear Mathematical Physics
28 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
26 Nuclear Physics. B
24 Duke Mathematical Journal
22 Proceedings of the Steklov Institute of Mathematics
21 Journal of Soviet Mathematics
16 Journal of Mathematical Analysis and Applications
16 Chaos, Solitons and Fractals
16 Annales de l’Institut Fourier
16 Mathematische Annalen
15 Journal of Functional Analysis
15 Transactions of the American Mathematical Society
15 Differential Geometry and its Applications
15 Regular and Chaotic Dynamics
14 Inventiones Mathematicae
14 Acta Applicandae Mathematicae
14 Journal of Physics A: Mathematical and Theoretical
13 Studies in Applied Mathematics
12 Physics Letters. A
12 Reviews in Mathematical Physics
12 Journal of Differential Equations
10 Constructive Approximation
10 Journal of Nonlinear Science
10 International Journal of Geometric Methods in Modern Physics
9 International Journal of Modern Physics A
9 Nonlinearity
9 Physics Letters. B
9 Russian Mathematical Surveys
9 Annals of Physics
8 Communications on Pure and Applied Mathematics
8 Manuscripta Mathematica
8 Mathematical Physics, Analysis and Geometry
7 International Journal of Theoretical Physics
7 Reports on Mathematical Physics
7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
7 The Journal of Geometric Analysis
7 Bulletin of the American Mathematical Society. New Series
7 St. Petersburg Mathematical Journal
7 Annales Henri Poincaré
6 Journal of Applied Mathematics and Mechanics
6 Journal of Algebra
6 Mathematische Zeitschrift
6 Proceedings of the American Mathematical Society
6 Russian Mathematics
6 Russian Journal of Mathematical Physics
6 Selecta Mathematica. New Series
6 Communications in Nonlinear Science and Numerical Simulation
6 Differential Equations
5 Journal d’Analyse Mathématique
5 Journal of Fluid Mechanics
5 Ukrainian Mathematical Journal
5 Publications of the Research Institute for Mathematical Sciences, Kyoto University
5 Siberian Mathematical Journal
5 Topology and its Applications
5 Chaos
4 Computers & Mathematics with Applications
4 Computer Methods in Applied Mechanics and Engineering
4 Journal of Computational Physics
4 Acta Mathematica
4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
4 Applied Mathematics and Computation
4 Compositio Mathematica
4 Journal of Computational and Applied Mathematics
4 Journal für die Reine und Angewandte Mathematik
4 Mathematische Nachrichten
4 Transactions of the Moscow Mathematical Society
4 Annals of Global Analysis and Geometry
4 International Journal of Mathematics
4 Aequationes Mathematicae
4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
4 Bulletin des Sciences Mathématiques
4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
4 Advances in Mathematical Physics
4 Ufimskiĭ Matematicheskiĭ Zhurnal
4 Arnold Mathematical Journal
3 Modern Physics Letters A
3 Applicable Analysis
3 Archive for Rational Mechanics and Analysis
3 Communications in Algebra
3 Journal of Statistical Physics
3 Mathematics of Computation
3 Geometriae Dedicata
3 Publications Mathématiques
3 International Journal of Mathematics and Mathematical Sciences
3 Tohoku Mathematical Journal. Second Series
3 Discrete & Computational Geometry
3 Journal of the American Mathematical Society
3 Numerical Algorithms
3 Journal de Mathématiques Pures et Appliquées. Neuvième Série
...and 155 more Serials
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Cited in 60 Fields

661 Dynamical systems and ergodic theory (37-XX)
586 Partial differential equations (35-XX)
347 Algebraic geometry (14-XX)
328 Differential geometry (53-XX)
313 Quantum theory (81-XX)
223 Ordinary differential equations (34-XX)
122 Global analysis, analysis on manifolds (58-XX)
122 Mechanics of particles and systems (70-XX)
98 Nonassociative rings and algebras (17-XX)
84 Fluid mechanics (76-XX)
73 Several complex variables and analytic spaces (32-XX)
69 Operator theory (47-XX)
68 Special functions (33-XX)
66 Functions of a complex variable (30-XX)
65 Relativity and gravitational theory (83-XX)
54 Statistical mechanics, structure of matter (82-XX)
38 Manifolds and cell complexes (57-XX)
37 Numerical analysis (65-XX)
30 Mechanics of deformable solids (74-XX)
28 Topological groups, Lie groups (22-XX)
28 Difference and functional equations (39-XX)
24 Number theory (11-XX)
23 Algebraic topology (55-XX)
22 Linear and multilinear algebra; matrix theory (15-XX)
22 Associative rings and algebras (16-XX)
22 Group theory and generalizations (20-XX)
20 Probability theory and stochastic processes (60-XX)
18 Combinatorics (05-XX)
18 Optics, electromagnetic theory (78-XX)
16 Functional analysis (46-XX)
13 Calculus of variations and optimal control; optimization (49-XX)
12 Harmonic analysis on Euclidean spaces (42-XX)
12 Systems theory; control (93-XX)
11 Computer science (68-XX)
10 Commutative algebra (13-XX)
10 Convex and discrete geometry (52-XX)
8 Field theory and polynomials (12-XX)
7 Geometry (51-XX)
6 Category theory; homological algebra (18-XX)
6 Potential theory (31-XX)
6 General topology (54-XX)
6 Geophysics (86-XX)
5 History and biography (01-XX)
5 Integral equations (45-XX)
5 Biology and other natural sciences (92-XX)
4 Approximations and expansions (41-XX)
4 Abstract harmonic analysis (43-XX)
4 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
4 Information and communication theory, circuits (94-XX)
3 General and overarching topics; collections (00-XX)
3 Measure and integration (28-XX)
3 Classical thermodynamics, heat transfer (80-XX)
2 Mathematical logic and foundations (03-XX)
2 Real functions (26-XX)
2 Statistics (62-XX)
2 Operations research, mathematical programming (90-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Sequences, series, summability (40-XX)
1 Integral transforms, operational calculus (44-XX)
1 Astronomy and astrophysics (85-XX)

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