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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. A.; Dubrovin, Boris; Dubrovin, B.; Dubrovin, Boris A.
Further Spellings: Дубровин Борис Анатольевич
Homepage: http://people.sissa.it/~dubrovin/
External Links: MGP · ORCID · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef
Documents Indexed: 122 Publications since 1973, including 13 Books
3 Contributions as Editor
Biographic References: 4 Publications
Co-Authors: 59 Co-Authors with 81 Joint Publications
2,014 Co-Co-Authors
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
3 Moscow Mathematical Journal
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 IMRN. International Mathematics Research Notices
2 Journal of Nonlinear Science
2 Selecta Mathematica. New Series
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 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
1 SIAM Journal on Applied Mathematics
1 Nuclear Physics. B. Proceedings Supplements
1 Mathematical Research Letters
1 Documenta Mathematica
1 Advances in Theoretical and Mathematical Physics
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 Open

108 Publications have been cited 2,875 times in 1,891 Documents Cited by Year
Geometry of 2D topological field theories. Zbl 0841.58065
Dubrovin, Boris
311
1996
Theta functions and non-linear equations. Zbl 0549.58038
Dubrovin, B. A.
165
1981
Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory. Zbl 0712.58032
Dubrovin, B. A.; Novikov, S. P.
148
1989
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.
120
1976
Nonlinear equations of Korteweg-de Vries type, finite-band linear operators and abelian varieties. (Nichtlineare Gleichungen Korteweg-de Vriesschen Typs, endlichzonige lineare Operatoren und Abelsche Mannigfaltigkeiten.) Zbl 0326.35011
Dubrovin, B. A.; Matveev, V. B.; Novikov, S. P.
116
1976
Theta-functions and non-linear equations. Zbl 0478.58038
Dubrovin, B. A.
94
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.
90
1983
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.
76
1992
On Poisson brackets of hydrodynamic type. Zbl 0591.58012
Dubrovin, B. A.; Novikov, S. P.
71
1984
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.
71
1984
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.
68
1985
Painlevé transcendents in two-dimensional topological field theory. Zbl 1026.34095
Dubrovin, Boris
65
1999
Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation. Zbl 0923.58060
Dubrovin, Boris; Zhang, Youjin
61
1998
Monodromy of certain Painlevé-VI transcendents and reflection groups. Zbl 0960.34075
Dubrovin, B.; Mazzocco, M.
57
2000
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.
51
1986
Periodic problems for the Korteweg-de Vries equation in the class of finite band potentials. Zbl 0358.35022
Dubrovin, B. A.
51
1976
On Hamiltonian perturbations of hyperbolic systems of conservation laws. II: Universality of critical behaviour. Zbl 1109.35070
Dubrovin, Boris
50
2006
The extended Toda hierarchy. Zbl 1076.37055
Carlet, Guido; Dubrovin, Boris; Zhang, Youjin
50
2004
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.
48
2009
Geometry and integrability of topological-antitopological fusion. Zbl 0771.53042
Dubrovin, B.
48
1993
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
46
2006
Integrable systems. I. Zbl 0780.58019
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
45
1985
Inverse problem for periodic finite-zoned potentials in the theory of scattering. Zbl 0315.35072
Dubrovin, B. A.
39
1975
Geometry and analytic theory of Frobenius manifolds. Zbl 0916.32018
Dubrovin, Boris
39
1998
Extended affine Weyl groups and Frobenius manifolds. Zbl 0964.32020
Dubrovin, Boris; Zhang, Youjin
39
1998
The Schrödinger equation in a periodic field and Riemann surfaces. Zbl 0441.35021
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
39
1976
On almost duality for Frobenius manifolds. Zbl 1063.53092
Dubrovin, Boris
36
2004
Hamiltonian formalism of Whitham-type hierarchies and topological Landau- Ginsburg models. Zbl 0753.58039
Dubrovin, B. A.
35
1992
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.
33
1990
Frobenius manifolds and Virasoro constraints. Zbl 0963.81066
Dubrovin, Boris; Zhang, Youjin
29
1999
Virasoro symmetries of the extended Toda hierarchy. Zbl 1071.37054
Dubrovin, Boris; Zhang, Youjin
29
2004
Modern geometry. (Современная геометрия.) Zbl 0433.53001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
26
1980
Real two-zone solutions of the sine-Gordon equation. Zbl 0554.35100
Dubrovin, B. A.; Natanzon, S. M.
26
1982
On universality of critical behaviour in Hamiltonian PDEs. Zbl 1172.35001
Dubrovin, Boris
25
2008
Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures. Zbl 1153.37032
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
22
2008
Canonical structure and symmetries of the Schlesinger equations. Zbl 1146.32005
Dubrovin, Boris; Mazzocco, Marta
22
2007
Completely integrable Hamiltonian systems associated with matrix operators and abelian varieties. Zbl 0413.58012
Dubrovin, B. A.
21
1978
Flat pencils of metrics and Frobenius manifolds. Zbl 0963.53054
Dubrovin, Boris
21
1998
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
20
2016
Integrable systems and classification of 2-dimensional topological field theories. Zbl 0824.58029
Dubrovin, B.
19
1993
Matrix finite-zone operators. Zbl 0561.58043
Dubrovin, B. A.
19
1985
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.
18
1974
Differential geometry of the space of orbits of a Coxeter group. Zbl 0962.53049
Dubrovin, Boris
18
1998
Real theta-function solutions of the Kadomtsev-Petviashvili equation. Zbl 0672.35072
Dubrovin, B. A.; Natanzon, S. M.
18
1988
Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. Zbl 1335.53114
Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin
17
2016
Numerical study of breakup in generalized Korteweg-de Vries and Kawahara equations. Zbl 1231.65175
Dubrovin, B.; Grava, T.; Klein, C.
15
2011
Minimal Liouville gravity correlation numbers from Douglas string equation. Zbl 1333.83172
Belavin, Alexander; Dubrovin, Boris; Mukhametzhanov, Baur
14
2014
On the critical behavior in nonlinear evolutionary PDEs with small viscosity. Zbl 1263.35019
Dubrovin, B.; Elaeva, M.
14
2012
Infinite-dimensional Frobenius manifolds for \(2+1\) integrable systems. Zbl 1208.53090
Carlet, Guido; Dubrovin, Boris; Mertens, Luca Philippe
13
2011
Three-phase solutions of the Kadomtsev-Petviashvili equation. Zbl 0893.35112
Dubrovin, B. A.; Flickinger, Ron; Segur, Harvey
12
1997
Modern geometry. Methods of homology theory. (Современная геометрия. Методы теории гомологий.) Zbl 0582.55001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
12
1984
Dynamical systems. IV: Integrable systems. Zbl 0591.58013
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
12
1985
Generating series for GUE correlators. Zbl 1380.37126
Dubrovin, Boris; Yang, Di
12
2017
Hamiltonian PDEs: deformations, integrability, solutions. Zbl 1221.37112
Dubrovin, B.
11
2010
Isomonodromy deformations at an irregular singularity with coalescing eigenvalues. Zbl 1416.34079
Cotti, Giordano; Dubrovin, Boris; Guzzetti, Davide
11
2019
Tau-structure for the double ramification hierarchies. Zbl 1431.53095
Buryak, Alexandr; Dubrovin, Boris; Guéré, Jérémy; Rossi, Paolo
11
2018
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
10
2019
Ground states in a periodic field. Magnetic Bloch functions and vector bundles. Zbl 0489.46055
Dubrovin, B. A.; Novikov, S. P.
10
1980
On critical behaviour in systems of Hamiltonian partial differential equations. Zbl 1321.35208
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio
10
2015
Ein periodisches Problem für die Korteweg-de Vries-Gleichung in der Klasse der endlich-zonalen Potentiale. Zbl 0338.35022
Dubrovin, B. A.
9
1975
Differential geometry of strongly integrable systems of hydrodynamic type. Zbl 0850.76008
Dubrovin, B. A.
9
1990
Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions. Zbl 1207.35032
Dubrovin, Boris
9
2009
Local moduli of semisimple Frobenius coalescent structures. Zbl 1442.53060
Cotti, Giordano; Dubrovin, Boris; Guzzetti, Davide
9
2020
Alternative Hamiltonian description for quantum systems. Zbl 1020.81606
Dubrovin, B. A.; Marmo, G.; Simoni, A.
9
1990
Simple Lie algebras and topological ODEs. Zbl 1406.17016
Bertola, Marco; Dubrovin, Boris; Yang, Di
9
2018
Hydrodynamics of soliton lattices. Zbl 0845.58027
Dubrovin, B. A.; Novikov, S. P.
7
1993
Symplectic field theory of a disk, quantum integrable systems, and Schur polynomials. Zbl 1342.81626
Dubrovin, Boris
6
2016
Poisson brackets on presymplectic manifolds. Zbl 0984.37500
Dubrovin, B. A.; Giordano, M.; Marmo, G.; Simoni, A.
6
1993
On the reductions and classical solutions of the Schlesinger equations. Zbl 1356.32007
Dubrovin, Boris; Mazzocco, Marta
6
2007
Gromov-Witten invariants and integrable hierarchies of topological type. Zbl 1370.53060
Dubrovin, B.
6
2014
Classical Hurwitz numbers and related combinatorics. Zbl 1411.14059
Dubrovin, Boris; Yang, Di; Zagier, Don
6
2017
On critical behaviour in generalized Kadomtsev-Petviashvili equations. Zbl 1415.37095
Dubrovin, B.; Grava, T.; Klein, C.
6
2016
Bihamiltonian cohomologies and integrable hierarchies. II: The tau structures. Zbl 1403.37072
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
6
2018
Gromov-Witten invariants of the Riemann sphere. Zbl 1453.14133
Dubrovin, Boris; Yang, Di; Zagier, Don
5
2020
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
On the genus two free energies for semisimple Frobenius manifolds. Zbl 1325.53114
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
5
2012
Separation of variables for linear Lax algebras and classical \(r\)-matrices. Zbl 1403.37067
Dubrovin, B.; Skrypnyk, T.
5
2018
Topological and algebraic geometry methods in contemporary mathematical physics. II. Zbl 0534.58002
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
5
1982
On cubic Hodge integrals and random matrices. Zbl 1439.14091
Dubrovin, Boris; Yang, Di
5
2017
Geometry of Hamiltonian evolutionary systems. Zbl 0936.37022
Dubrovin, Boris A.
4
1991
Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory. Zbl 0947.35117
Dubrovin, Boris
4
1998
Integrable systems of double ramification type. Zbl 1464.37071
Buryak, Alexandr; Dubrovin, Boris; Guéré, Jérémy; Rossi, Paolo
4
2020
The Kadomtsev-Petviashvili equation and the relations between the periods of holomorphic differentials on Riemann surfaces. Zbl 0501.14016
Dubrovin, B. A.
4
1982
On an isomonodromy deformation equation without the Painlevé property. Zbl 1322.34102
Dubrovin, B.; Kapaev, A.
4
2014
Theory of operators and real algebraic geometry. Zbl 0773.35045
Dubrovin, B. A.
3
1987
Hodge-GUE correspondence and the discrete KdV equation. Zbl 1455.37056
Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin
3
2020
A Riemann-Hilbert approach to the Heun equation. Zbl 1404.34100
Dubrovin, Boris; Kapaev, Andrei
3
2018
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.
3
1982
On Gromov-Witten invariants of \(\mathbb{P}^1\). Zbl 1441.14180
Dubrovin, Boris; Yang, Di
3
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
Riemann surfaces and nonlinear equations. Textbook. Part 1. (Rimanovy poverkhnosti i nelinejnye uravneniya. Uchebnoe posobie. Chast’ 1.) Zbl 0692.35079
Dubrovin, B. A.
2
1986
Hamiltonian PDEs and Frobenius manifolds. Zbl 1170.53072
Dubrovin, B. A.
2
2008
Kadomtsev-Petviashvili equation and relations between the periods of holomorphic differentials on Riemann surfaces. Zbl 0477.14018
Dubrovin, B. A.
2
1981
Matrix resolvent and the discrete KdV hierarchy. Zbl 1454.37065
Dubrovin, Boris; Yang, Di
2
2020
Separation of variables for quadratic algebras and skew-symmetric classical \(r\)-matrices. Zbl 1436.70005
Dubrovin, B.; Skrypnyk, T.
2
2019
Differential-geometric Poisson brackets on a lattice. Zbl 0711.58027
Dubrovin, B. A.
2
1989
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.
2
1982
Topology. Methodical instructions. (Topologiya. Metodicheskie ukazaniya.) Zbl 0698.54001
Dubrovin, B. A.; Solov’ev, Yu. P.
1
1988
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
Simple Lie algebras, Drinfeld-Sokolov hierarchies, and multi-point correlation functions. Zbl 1482.37066
Bertola, Marco; Dubrovin, Boris; Yang, Di
1
2021
On tau-functions for the KdV hierarchy. Zbl 1458.14061
Dubrovin, Boris; Yang, Di; Zagier, Don
1
2021
Local moduli of semisimple Frobenius coalescent structures. Zbl 1442.53060
Cotti, Giordano; Dubrovin, Boris; Guzzetti, Davide
9
2020
Gromov-Witten invariants of the Riemann sphere. Zbl 1453.14133
Dubrovin, Boris; Yang, Di; Zagier, Don
5
2020
Integrable systems of double ramification type. Zbl 1464.37071
Buryak, Alexandr; Dubrovin, Boris; Guéré, Jérémy; Rossi, Paolo
4
2020
Hodge-GUE correspondence and the discrete KdV equation. Zbl 1455.37056
Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin
3
2020
Matrix resolvent and the discrete KdV hierarchy. Zbl 1454.37065
Dubrovin, Boris; Yang, Di
2
2020
Algebraic spectral curves over \(\mathbb{Q}\) and their tau-functions. Zbl 1484.14073
Dubrovin, Boris
1
2020
Isomonodromy deformations at an irregular singularity with coalescing eigenvalues. Zbl 1416.34079
Cotti, Giordano; Dubrovin, Boris; Guzzetti, Davide
11
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
10
2019
On Gromov-Witten invariants of \(\mathbb{P}^1\). Zbl 1441.14180
Dubrovin, Boris; Yang, Di
3
2019
Separation of variables for quadratic algebras and skew-symmetric classical \(r\)-matrices. Zbl 1436.70005
Dubrovin, B.; Skrypnyk, T.
2
2019
Tau-structure for the double ramification hierarchies. Zbl 1431.53095
Buryak, Alexandr; Dubrovin, Boris; Guéré, Jérémy; Rossi, Paolo
11
2018
Simple Lie algebras and topological ODEs. Zbl 1406.17016
Bertola, Marco; Dubrovin, Boris; Yang, Di
9
2018
Bihamiltonian cohomologies and integrable hierarchies. II: The tau structures. Zbl 1403.37072
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
6
2018
Separation of variables for linear Lax algebras and classical \(r\)-matrices. Zbl 1403.37067
Dubrovin, B.; Skrypnyk, T.
5
2018
A Riemann-Hilbert approach to the Heun equation. Zbl 1404.34100
Dubrovin, Boris; Kapaev, Andrei
3
2018
Generating series for GUE correlators. Zbl 1380.37126
Dubrovin, Boris; Yang, Di
12
2017
Classical Hurwitz numbers and related combinatorics. Zbl 1411.14059
Dubrovin, Boris; Yang, Di; Zagier, Don
6
2017
On cubic Hodge integrals and random matrices. Zbl 1439.14091
Dubrovin, Boris; Yang, Di
5
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
20
2016
Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. Zbl 1335.53114
Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin
17
2016
Symplectic field theory of a disk, quantum integrable systems, and Schur polynomials. Zbl 1342.81626
Dubrovin, Boris
6
2016
On critical behaviour in generalized Kadomtsev-Petviashvili equations. Zbl 1415.37095
Dubrovin, B.; Grava, T.; Klein, C.
6
2016
On critical behaviour in systems of Hamiltonian partial differential equations. Zbl 1321.35208
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio
10
2015
Minimal Liouville gravity correlation numbers from Douglas string equation. Zbl 1333.83172
Belavin, Alexander; Dubrovin, Boris; Mukhametzhanov, Baur
14
2014
Gromov-Witten invariants and integrable hierarchies of topological type. Zbl 1370.53060
Dubrovin, B.
6
2014
On an isomonodromy deformation equation without the Painlevé property. Zbl 1322.34102
Dubrovin, B.; Kapaev, A.
4
2014
On the critical behavior in nonlinear evolutionary PDEs with small viscosity. Zbl 1263.35019
Dubrovin, B.; Elaeva, M.
14
2012
On the genus two free energies for semisimple Frobenius manifolds. Zbl 1325.53114
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
5
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.
15
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.
48
2009
Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions. Zbl 1207.35032
Dubrovin, Boris
9
2009
On universality of critical behaviour in Hamiltonian PDEs. Zbl 1172.35001
Dubrovin, Boris
25
2008
Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures. Zbl 1153.37032
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin
22
2008
Hamiltonian PDEs and Frobenius manifolds. Zbl 1170.53072
Dubrovin, B. A.
2
2008
Canonical structure and symmetries of the Schlesinger equations. Zbl 1146.32005
Dubrovin, Boris; Mazzocco, Marta
22
2007
On the reductions and classical solutions of the Schlesinger equations. Zbl 1356.32007
Dubrovin, Boris; Mazzocco, Marta
6
2007
On Hamiltonian perturbations of hyperbolic systems of conservation laws. II: Universality of critical behaviour. Zbl 1109.35070
Dubrovin, Boris
50
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
46
2006
The extended Toda hierarchy. Zbl 1076.37055
Carlet, Guido; Dubrovin, Boris; Zhang, Youjin
50
2004
On almost duality for Frobenius manifolds. Zbl 1063.53092
Dubrovin, Boris
36
2004
Virasoro symmetries of the extended Toda hierarchy. Zbl 1071.37054
Dubrovin, Boris; Zhang, Youjin
29
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.
57
2000
Painlevé transcendents in two-dimensional topological field theory. Zbl 1026.34095
Dubrovin, Boris
65
1999
Frobenius manifolds and Virasoro constraints. Zbl 0963.81066
Dubrovin, Boris; Zhang, Youjin
29
1999
Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation. Zbl 0923.58060
Dubrovin, Boris; Zhang, Youjin
61
1998
Geometry and analytic theory of Frobenius manifolds. Zbl 0916.32018
Dubrovin, Boris
39
1998
Extended affine Weyl groups and Frobenius manifolds. Zbl 0964.32020
Dubrovin, Boris; Zhang, Youjin
39
1998
Flat pencils of metrics and Frobenius manifolds. Zbl 0963.53054
Dubrovin, Boris
21
1998
Differential geometry of the space of orbits of a Coxeter group. Zbl 0962.53049
Dubrovin, Boris
18
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
12
1997
Geometry of 2D topological field theories. Zbl 0841.58065
Dubrovin, Boris
311
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.
48
1993
Integrable systems and classification of 2-dimensional topological field theories. Zbl 0824.58029
Dubrovin, B.
19
1993
Hydrodynamics of soliton lattices. Zbl 0845.58027
Dubrovin, B. A.; Novikov, S. P.
7
1993
Poisson brackets on presymplectic manifolds. Zbl 0984.37500
Dubrovin, B. A.; Giordano, M.; Marmo, G.; Simoni, A.
6
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.
76
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.
33
1990
Differential geometry of strongly integrable systems of hydrodynamic type. Zbl 0850.76008
Dubrovin, B. A.
9
1990
Alternative Hamiltonian description for quantum systems. Zbl 1020.81606
Dubrovin, B. A.; Marmo, G.; Simoni, A.
9
1990
Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory. Zbl 0712.58032
Dubrovin, B. A.; Novikov, S. P.
148
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.
18
1988
Topology. Methodical instructions. (Topologiya. Metodicheskie ukazaniya.) 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.
51
1986
Riemann surfaces and nonlinear equations. Textbook. Part 1. (Rimanovy poverkhnosti i nelinejnye uravneniya. Uchebnoe posobie. Chast’ 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.
68
1985
Integrable systems. I. Zbl 0780.58019
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
45
1985
Matrix finite-zone operators. Zbl 0561.58043
Dubrovin, B. A.
19
1985
Dynamical systems. IV: Integrable systems. Zbl 0591.58013
Dubrovin, B. A.; Krichever, I. M.; Novikov, S. P.
12
1985
On Poisson brackets of hydrodynamic type. Zbl 0591.58012
Dubrovin, B. A.; Novikov, S. P.
71
1984
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.
71
1984
Modern geometry. Methods of homology theory. (Современная геометрия. Методы теории гомологий.) Zbl 0582.55001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
12
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.
90
1983
Real two-zone solutions of the sine-Gordon equation. Zbl 0554.35100
Dubrovin, B. A.; Natanzon, S. M.
26
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
The Kadomtsev-Petviashvili equation and the relations between the periods of holomorphic differentials on Riemann surfaces. Zbl 0501.14016
Dubrovin, B. A.
4
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.
3
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.
2
1982
Theta functions and non-linear equations. Zbl 0549.58038
Dubrovin, B. A.
165
1981
Theta-functions and non-linear equations. Zbl 0478.58038
Dubrovin, B. A.
94
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. (Современная геометрия.) Zbl 0433.53001
Dubrovin, B. A.; Novikov, S. P.; Fomenko, A. T.
26
1980
Ground states in a periodic field. Magnetic Bloch functions and vector bundles. Zbl 0489.46055
Dubrovin, B. A.; Novikov, S. P.
10
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.
21
1978
...and 8 more Documents
all top 5

Cited by 1,731 Authors

36 Dubrovin, Boris Anatol’evich
35 Geng, Xianguo
31 Ferapontov, Evgeny Vladimirovich
29 Zhang, Youjin
25 Pavlov, Maxim V.
23 Liu, Siqi
22 Strachan, Ian A. B.
21 Klein, Christian
19 Grava, Tamara
18 Grinevich, Pëtr Georgievich
18 Krichever, Igor’ Moiseevich
18 Veselov, Alexander Petrovich
17 Mokhov, Oleg I.
16 Shadrin, Sergey V.
16 Yang, Di
15 Gesztesy, Fritz
15 Lorenzoni, Paolo
14 Dragović, Vladimir
14 Konopelchenko, Boris Georgievich
14 Milanov, Todor E.
14 Novikov, Sergeĭ Petrovich
14 Simon, Barry
13 Rossi, Paolo
12 Buryak, Alexandr Y.
12 El, Gennady A.
12 He, Guoliang
12 Natanzon, Sergei M.
12 Smirnov, Alexander O.
11 Bertola, Marco
11 Johnson, Russell Allan
11 Shamolin, Maksim Vladimirovich
11 Wu, Chaozhong
10 Bukhshtaber, Viktor Matveevich
10 Carlet, Guido
10 Korotkin, Dmitrii A.
10 Marmo, Giuseppe
10 Miller, Peter D.
10 Shabat, Alekseĭ Borisovich
10 Vitolo, Raffaele F.
9 Abenda, Simonetta
9 Bogoyavlenskij, Oleg Igorevich
9 Enolskiĭ, Viktor Zelikovich
9 Falqui, Gregorio
9 Fan, Engui
9 Guzzetti, Davide
9 Li, Chuanzhong
9 Novikov, Roman G.
9 Ortenzi, Giovanni
9 Stoilov, Nikola M.
9 Taimanov, Iskander Asanovich
9 Takasaki, Kanehisa
9 Zeng, Xin
9 Zhai, Yunyun
8 Bobenko, Alexander Ivanovich
8 Hertling, Claus
8 Iritani, Hiroshi
8 Mironov, Andreĭ Evgen’evich
8 Prykarpatsky, Anatoliy Karolevych
8 Raimondo, Andrea
8 Schäfer, Lars
8 Takahashi, Atsushi
8 Tu, Minghsien
8 Varchenko, Alexander Nikolaevich
8 Wei, Jiao
8 Wu, Lihua
7 Agafonov, Sergey I.
7 Belavin, Aleksandr Abramovich
7 Belavin, Vladimir A.
7 Brini, Andrea
7 Casati, Matteo
7 Chen, Jinbing
7 Dobrokhotov, Sergei Yurievich
7 Fedorov, Yuri N.
7 Harnad, John
7 Lisovyy, Oleg
7 Masoero, Davide
7 Mazzocco, Marta
7 Novokshenov, Viktor Yur’evich
7 Odesskii, Alexander
7 Pedroni, Marco
7 Shramchenko, Vasilisa
7 Sokolov, Vladimir Vyacheslavovich
7 Suleĭmanov, Bulat Irekovich
7 Xue, Bo
7 Zampogni, Luca
7 Zeng, Yunbo
6 Cecotti, Sergio
6 Chalykh, Oleg A.
6 Chekhov, Leonid O.
6 Claeys, Tom
6 Cotti, Giordano
6 David, Liana
6 Deconinck, Bernard
6 Dunin-Barkovskiĭ, Petr Igorevich
6 Hou, Yu
6 Khasanov, Aknazar Bekdurdievich
6 Korotyaev, Evgeny L.
6 Kuksin, Sergeĭ B.
6 Lee, Niann-Chern
6 Lin, Chang-Shou
...and 1,631 more Authors
all top 5

Cited in 274 Serials

137 Communications in Mathematical Physics
115 Journal of Mathematical Physics
113 Journal of Geometry and Physics
93 Theoretical and Mathematical Physics
78 Letters in Mathematical Physics
69 Physica D
60 Functional Analysis and its Applications
50 Advances in Mathematics
41 Journal of Mathematical Sciences (New York)
38 Journal of High Energy Physics
35 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
31 Mathematical Notes
29 Journal of Nonlinear Mathematical Physics
24 Duke Mathematical Journal
23 Proceedings of the Steklov Institute of Mathematics
22 Nuclear Physics. B
21 Journal of Soviet Mathematics
18 Nonlinearity
16 Chaos, Solitons and Fractals
16 Mathematische Annalen
16 Differential Geometry and its Applications
16 Regular and Chaotic Dynamics
15 Journal of Mathematical Analysis and Applications
15 Annales de l’Institut Fourier
15 Transactions of the American Mathematical Society
15 Journal of Nonlinear Science
14 Reviews in Mathematical Physics
14 Inventiones Mathematicae
14 Acta Applicandae Mathematicae
14 Journal of Physics A: Mathematical and Theoretical
13 Journal of Differential Equations
13 Journal of Functional Analysis
13 Studies in Applied Mathematics
11 Russian Mathematical Surveys
10 Physics Letters. A
10 Constructive Approximation
10 International Journal of Geometric Methods in Modern Physics
9 International Journal of Modern Physics A
9 Selecta Mathematica. New Series
9 Mathematical Physics, Analysis and Geometry
8 Communications on Pure and Applied Mathematics
8 Manuscripta Mathematica
8 The Journal of Geometric Analysis
8 Russian Mathematics
8 St. Petersburg Mathematical Journal
8 Differential Equations
7 International Journal of Theoretical Physics
7 Physics Letters. B
7 Reports on Mathematical Physics
7 Mathematische Zeitschrift
7 Annals of Physics
7 Bulletin of the American Mathematical Society. New Series
7 Russian Journal of Mathematical Physics
7 Annales Henri Poincaré
7 Ufimskiĭ Matematicheskiĭ Zhurnal
6 Journal of Applied Mathematics and Mechanics
6 Journal of Algebra
6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
6 Proceedings of the American Mathematical Society
6 Publications of the Research Institute for Mathematical Sciences, Kyoto University
6 Communications in Nonlinear Science and Numerical Simulation
5 Journal d’Analyse Mathématique
5 Journal of Fluid Mechanics
5 Ukrainian Mathematical Journal
5 Compositio Mathematica
5 Journal für die Reine und Angewandte Mathematik
5 Siberian Mathematical Journal
5 Transactions of the Moscow Mathematical Society
5 Topology and its Applications
5 International Journal of Mathematics
5 Chaos
5 Advances in Mathematical Physics
4 Applicable Analysis
4 Journal of Computational Physics
4 Acta Mathematica
4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
4 Applied Mathematics and Computation
4 Geometriae Dedicata
4 Journal of Computational and Applied Mathematics
4 Mathematische Nachrichten
4 Annals of Global Analysis and Geometry
4 Numerical Algorithms
4 Aequationes Mathematicae
4 Journal of Dynamics and Differential Equations
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 Science China. Mathematics
4 Analysis and Mathematical Physics
4 Arnold Mathematical Journal
4 European Journal of Mathematics
4 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
3 Archive for Rational Mechanics and Analysis
3 Communications in Algebra
3 Computers & Mathematics with Applications
3 Computer Methods in Applied Mechanics and Engineering
3 Journal of Statistical Physics
3 Wave Motion
3 Mathematics of Computation
3 Publications Mathématiques
...and 174 more Serials
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Cited in 60 Fields

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

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