Boris Dubrovin Publications

Selected Papers of Boris Dubrovin

  1. Bihamiltonian cohomologies and integrable hierarchies II: the tau structures (pdf), arXiv:1701.03222 (with Si-Qi Liu,Youjin Zhang)

  2. Hodge-GUE correspondence and the discrete KdV equation (pdf), arXiv:1612.02333 (with Si-Qi Liu, Di Yang, Youjin Zhang)

  3. Simple Lie algebras, Drinfeld-Sokolov hierarchies, and multipoint correlation functions (pdf), arXiv:1610.07534 (with Marco Bertola, Di Yang)

  4. Integrable systems of double ramification type (pdf), arXiv:1609.04059 (with A.Buryak, J.Guéré, P.Rossi)

  5. On cubic Hodge integrals and random matrices (pdf), arXiv:1606.03720 (with Di Yang)

  6. Generating series for GUE correlators (pdf), arXiv:1604.07628 (with Di Yang)

  7. Tau-structures for the double ramification hierarchies (pdf), arXiv:1602.05423 (with A.Buryak, J.Guéré, P.Rossi)

  8. On critical behaviour in generalised Kadomtsev - Petviashvili equations (pdf), Physica D 333 (2016) 157-170 (with T.Grava, C.Klein)

  9. Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau - Ginzburg superpotentials (pdf), arXiv:1510.08690 (with Ian A.B.Strachan, Youjin Zhang, Dafeng Zuo)

  10. Simple Lie algebras and topological ODEs (pdf), arXiv:1508.03750, to appear in IMRN (with Marco Bertola, Di Yang)

  11. Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline{\mathcal M}_{g,n}$ (pdf), Physica D 327 (2016) 30-57 (with M.Bertola and Di Yang)

  12. Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs (pdf), Adv. Math. 293 (2016) 382-435 (with Si-Qi Liu, Di Yang, Youjin Zhang)

  13. Symplectic field theory of a disk, quantum integrable systems, and Schur polynomials (pdf), Ann. Henri Poincaré 17 (2016) no. 7, 1595-1613

  14. On critical behaviour in systems of Hamiltonian partial differential equations (pdf), J. Nonlinear Sci. 25 (2015) 631-707 (with T.Grava, C.Klein, A.Moro)

  15. Gromov - Witten invariants and integrable hierarchies of topological type (pdf), Amer. Math. Transl. 234 (2014) 141-171

  16. Minimal Liouville gravity correlation numbers from Douglas string equation (pdf), JHEP 01(2014) 156 (with A.Belavin and B.Mukhametzhanov)

  17. On an isomonodromy deformation equation without the Painlevé property (pdf), Russ. J. Math. Phys. 21 no. 1 (2014) 9-35 (with A.Kapaev)

  18. On the critical behavior in nonlinear evolutionary PDEs with small viscocity (pdf), Russ. J. Math. Phys. 19:4 (2012) 13-22 (with M.Elaeva)

  19. On the genus two free energies for semisimple Frobenius manifolds (pdf), Russ. J. Math. Phys. 19:3 (2012) 1-10 (with Si-Qi Liu and Youjin Zhang)

  20. Classical double, R-operators, and negative flows of integrable hierarchies (pdf), Theor. Math. Phys. 172 (2012) 911-931 (with T.Skrypnyk)

  21. Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems (pdf), Math. Ann. 349 (2011) 75-115 (with G.Carlet and L.P.Mertens),

  22. Numerical study of breakup in generalized Korteweg - de Vries and Kawahara equations (pdf), SIAM. J. Appl. Math. 71 (2011) 983-1008 (with T.Grava and C.Klein)

  23. Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations (pdf), Funct. Anal. Appl. 45:4 (2011) 278-290 (with M.Pavlov and S.Zykov)

  24. Hamiltonian PDEs: deformations, integrability, solutions (pdf), J. Phys. A: Math. Theor. 43 (2010) 434002

  25. On universality of critical behaviour in the focusing nonlinear Schroedinger equation, elliptic umbilic catastrophe and the tritronquée solution to the Painlevé-I equation (pdf), J. Nonlinear Sci. 19 (2009) 57-94 (with T.Grava and C.Klein)

  26. Hamiltonian Perturbations of Hyperbolic PDEs: from Classification Results to the Properties of Solutions, (pdf) In: New Trends in Mathematical Physics. Selected contributions of the XVth International Congress on Mathematical Physics , Sidoravicius, Vladas (Ed.), Springer Netherlands, 2009., pp. 231-276.

  27. Frobenius manifolds and central invariants for the Drinfeld - Sokolov bihamiltonian structures (pdf), Adv. Math. 219 (2008) 780-837 (with Si-Qi Liu, Youjin Zhang).

  28. Hamiltonian partial differential equations and Frobenius manifolds (pdf), Russ. Math. Surveys 63 (2008) 999-1010.

  29. On universality of critical behaviour in Hamiltonian PDEs (pdf), Amer. Math. Soc. Transl. 224 (2008) 59-109.

  30. On the reductions and classical solutions of the Schlesinger equations (pdf), Differential equations and quantum groups, IRMA Lect. Math. Theor. Phys. 9 (2007) 157-187. Eur. Math. Soc., Zuerich, 2007 (with M. Mazzocco).

  31. Canonical structure and symmetries of the Schlesinger equations (pdf) , Comm. Math. Phys. 271 (2007) 289--373 (with Marta Mazzocco).

  32. On Hamiltonian perturbations of hyperbolic systems of conservation laws II: universality of critical behaviour (pdf), Comm. Math. Phys. 267 (2006) 117 - 139.

  33. WDVV equations and Frobenius manifolds (pdf), Encyclopedia of Mathematical Physics , eds. J.-P. Françoise, G.L. Naber and Tsou S.T., Oxford: Elsevier, 2006, Vol. 1, p. 438-447.

  34. On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasi-triviality of bi-hamiltonian perturbations (pdf), Comm. in Pure Appl. Math. 59 (2006) 559 - 615 (with Si-Qi Liu, Youjin Zhang).

  35. Extended affine Weyl groups and Frobenius manifolds -- II (pdf) , math.DG/0502365 (23 pages) (with Youjin Zhang, Dafeng Zuo).

  36. On analytic families of invariant tori for PDEs (pdf), Astérisque 297 (2004) 35-65.

  37. Virasoro Symmetries of the Extended Toda Hierarchy (pdf), Comm. Math. Phys. 250 (2004) 161-193 (with Youjin Zhang).

  38. On almost duality for Frobenius manifolds (pdf), Amer. Math. Soc. Transl. 212 (2004) 75-132.

  39. The Extended Toda Hierarchy (pdf), Moscow Math. J. 4 (2004) 313-332 (with Guido Carlet and Youjin Zhang).

  40. Monodromy of certain Painlevé-VI transcendents and reflection groups (pdf), Inventiones Math. 141 (2000) 55-147 (with M.Mazzocco).

  41. Painlevé transcendents and topological field theory (pdf), In: The Painlevé Property: One Century Later. R.Conte (Ed.), Springer Verlag, 1999, p. 287-412

  42. Frobenius manifolds and Virasoro constraints (pdf), Selecta Mathematica 5 (1999) 423-466 (with Youjin Zhang).

  43. Recurrent procedure for the determination of the free energy ε^2 expansion in the topological string theory (arXiv:solv-int/990400) (with A.Maltsev).

  44. Geometry and analytic theory of Frobenius manifolds (pdf) , Proceedings of ICM98 2 (1998) 315-326.

  45. Flat pencils of metrics and Frobenius manifolds (pdf), Proceedings of 1997 Taniguchi Symposium "Integrable Systems and Algebraic Geometry", Editors M.-H. Saito, Y.Shimizu and K.Ueno, 47-72. World Scientific, 1998.

  46. Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation (pdf), Comm. Math. Phys. 198 (1998) 311-361 (with Youjin Zhang).

  47. Extended Affine Weyl Groups and Frobenius Manifolds (pdf) , Compositio Math. 111 (1998) 167-219 (with Youjin Zhang).

  48. Functionals of the Peierls - Fröhlich Type and the Variational Principle for the Whitham Equations (pdf), In: Amer. Math. Soc. Transl. (2) 179 (1997) 35-44.

  49. Three-Phase Solutions of the Kadomtsev - Petviashvili Equation (pdf), Studies in Applied Math. 99 (1997) 137-203 (with R.Flickinger and H.Segur).

  50. Geometry of 2D topological field theories (pdf). In: Integrable Systems and Quantum Groups (Authors: R.Donagi, B.Dubrovin, E.Frenkel, E.Previato), Eds. M.Francaviglia, S.Greco, Springer Lecture Notes in Math. 1620 (1996), pp. 120 - 348.

  51. Integrable functional equations and algebraic geometry (pdf) , Duke Math. J. 76 (1994) 645-668 (with A.S.Fokas and P.M.Santini).

  52. Algebraic-geometrical Darboux coordinates in R-matrix formalism (pdf), Preprint SISSA 88/94/FM (with P.Diener).

  53. Geometry and integrability of topological-antitopological fusion (pdf), Commun. Math. Phys. 152 (1993) 539-564.

  54. Dispersion relations for non-linear waves and the Schottky problem (pdf). In: Important Developments In Soliton Theory , ed. A.S.Fokas and V.E.Zakharov, pp. 86 - 98. Springer Verlag, 1993.

  55. Time-dependent Schroedinger-like operators and related integrable models , Preprint LA-UR-93-4009, Los Alamos, 1993, 13 pages (with V.G.Makhankov).

  56. Differential geometry of the space of orbits of a Coxeter group (pdf). Preprint SISSA 29/93/FM, February 1993, 30 pp. Published in: Surveys in Differential Geometry , Vol. IV (1999), p. 181 - 212.

  57. Poisson brackets on presymplectic manifolds , Int. J. Mod. Phys. A8 (1993) 3747-3771 (with M.Giordano, G.Marmo and A.Simoni).

  58. Topological conformal field theory from the point of view of integrable systems (pdf). In: "Integrable Quantum Field Theories", Eds. L.Bonora, G.Mussardo, A.Schwimmer, L.Girardello, and M.Martellini, pp. 283 - 302. Plenum Press, 1993.

  59. Integrable systems and classification of 2D topological field theories (pdf). In: "Integrable Systems", The J.-L.Verdier Memorial Conference , Actes du Colloque International de Luminy. Eds. O.Babelon, P.Cartier, Y.Kosmann-Schwarzbach, pp. 313 - 359. Birkhäuser, 1993.

  60. Integrable systems in topological field theory (pdf), Nucl. Phys. B 379 (1992) 627-689.

  61. Hamiltonian formalism of Whitham-type hierarchies and topological Landau - Ginsburg models (pdf), Commun. Math. Phys. 145 (1992) 195-207.

  62. Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory (pdf). Preprint n.117, Scuola Normale Superiore, Pisa, November 1991, 31 pp. Published in: Surveys in Differential Geometry , Vol. IV (1999), p. 213 - 238.

  63. On differential geometry of strongly integrable systems of hydrodynamic type (pdf), Funktsionaln. Analiz i ego Prilozhenija 24:4 (1990) 25-30. English translation (pdf) in: Funct. Anal. Appl. 24 (1990) 280-285.

  64. Weakly perturbed soliton lattices. (pdf), Nucl. Phys. B (Proc. Suppl.) 18A (1990), 23-44.

  65. Alternative Hamiltonian description for quantum systems. Modern Physics Letters A 5:15 (1990) (with G.Marmo, A.Simoni).

  66. Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory (pdf), Uspekhi Matem. Nauk 44:6 (1989) 29-98. English translation (pdf) in: Russ. Math. Surveys 44:6 (1989) 35-124 (with S.P.Novikov).

  67. Differential-geometric Poisson brackets on a lattice (pdf), Funktsionaln. Analiz i ego Prilozhenija 23:2 (1989) 57-59. English translation (pdf) in: Funct. Anal. Appl. 23:2 (1989) 131-133.

  68. Exact solutions of non-stationary Schroedinger equation with self-consistent potential (pdf), Soviet J. Part. Nucl. 19:3 (1988) 579-621 (with. I.M.Krichever, T.M.Malanyuk, and V.G.Makhankov).

  69. Real theta-functional solutions of the Kadomtsev-Petviashvili equation (pdf), Izvestija Akad. Nauk SSSR, serija matem., 52:2 (1988) 267-286. English translation (pdf) in: Math. USSR Izvestia 32:2 (1989) 269-288 (with S.M.Natanzon).

  70. Theory of operators and real algebraic geometry. In: Global Analysis and Mathematical Physics (1987), Voronezh University Publishing House (English translation: Lecture Notes in Math. 1334 (1988), 42-59).

  71. Integrable systems. I (pdf). In: Sovremennye Problemy Matematiki. Fundamentalnye Napravleniya 4, VINITI, Moscow, 1985, 179-285 (with I.M.Krichever and S.P.Novikov). English translation: Encyclopaedia of Mathematical Sciences 4, 173-280.

  72. On Poisson brackets of hydrodynamic type (pdf), Soviet Math. Dokl. 279:2 (1984), 294-297 (with S.P.Novikov).

  73. Non-linear equations conected with matrix finite-gap operators. In: Nonlinear and Turbulent Processes in Physics 3 (1984), Gordon and Breach, NY.

  74. Spectrum of matrix finite-gap operators. Russian Math. Surv. 39:2 (1984).

  75. Matrix finite-gap operators (pdf). In: Sovremennye Problemy Matematiki, VINITI 23 (1983). 77-123. English transl. (pdf): J. Soviet Math. 28 (1985), 20-50.

  76. The Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov - Whitham averaging method (pdf), Soviet Math. Dokl. 270:4 (1983) 665-669 (with S.P.Novikov).

  77. Topological and algebraic geometrical methods in contemporary mathematical physics. II. In: Soviet Scientific Reviews, Vol. C3 (Mathematical Physics Reviews) (1982), 1-150 (with I.M.Krichever and S.P.Novikov).

  78. Algebraic-geometric Poisson brackets for real finite-gap solutions of the Sine-Gordon equation and the non-linear Schrödinger equation (pdf), Soviet Math. Dokl. 267:6 (1982) 1295-1300 (with S.P.Novikov).

  79. Analytic properties of spectral data for non-selfadjoint linear operators, associated with the real periodic solutions of the Sine-Gordon equation, Soviet Math. Dokl. 265:4 (1982) 789-793.

  80. Real two-gap solutions of the Sine-Gordon equation (pdf), Funktsionaln. Analiz i ego Prilozhenija 16:1 (1982) 27-43. English translation (pdf) in: Funct. Anal. Appl. 16:1 (1982), 21-33 (with S.M.Natanzon).

  81. Theta-functions and nonlinear equations (pdf), Uspekhi Matem. Nauk 36:2 (1981). English translation (pdf) in: Russian Math. Surv. 36:2 (1981), 11-92.

  82. The Kadomtsev -- Petviashvili equation and relations for the periods of holomorphic differentials on Riemann surfaces (pdf), Izvestija Akad. Nauk SSSR, serija matem. 45:5 (1981) 1015-1028. English translation (pdf) in: Math. USSR Izvestia 19:2 (1982) 285-296.

  83. Ground states in a periodic field. Magnetic Bloch functions and vector bundles (pdf), Soviet Math. Dokl. 253:6 (1980) (with S.P.Novikov).

  84. Ground states of a two-dimensional electron in periodic magnetic field (pdf), Soviet Phys. JETP 79:3 (1980) 1006-1016 (with S.P.Novikov).

  85. On the S.P.Novikov conjecture in the theory of theta-functions and nonlinear equations of the Korteweg - de Vries and Kadomtsev - Petviashvili type, Soviet Math. Dokl. 251:3 (1980) 541-544.

  86. Completely integrable Hamiltonian systems, associated with matrix operators, and Abelian varieties (pdf), Funktsionaln. Analiz i ego Prilozhenija 11:4 (1977) 28-41. English translation (pdf) in: Funct. Anal. Appl. 11:4 (1977) 265-277.

  87. Finite-zone linear differential operators and Abelian varieties (pdf), Uspekhi Matem. Nauk 31:4 (1976) 259-260.

  88. Non-linear equations of Korteweg -- de Vries type, finite-zone linear operators, and Abelian varieties (pdf), Uspekhi Matem. Nauk 31:1 (1976), 55-136. English translation (pdf) in: Russian Math. Surv. 31:1 (1976), 59-146 (with V.B.Matveev and S.P.Novikov).

  89. Schroedinger equation in magnetic field and Riemann surfaces (pdf), Soviet Math. Dokl. 229:1 (1976) (with I.M.Krichever and S.P.Novikov).

  90. Periodic problem for the Korteweg - de Vries equation in the class of finite-zone potentials (pdf), Funktsionaln. Analiz i ego Prilozhenija 9:3 (1975), 41-51. English translation (pdf) in: Funct. Anal. Appl. 9:3 (1975) 215-223.

  91. Inverse problem of scattering theory for periodic finite-zone potentials (pdf), Funktsionaln. Analiz i ego Prilozhenija 9:1 (1975) 65-66. English translation (pdf) in: Funct. Anal. Appl. 9:1 (1975) 61-62.

  92. Korteweg - de Vries equation and algebraic geometry, Russian Math. Surv. 29:9 (1974) (with S.P.Novikov).

  93. Periodic Korteweg - de Vries and Sturm - Liouville problems. Their connection with algebraic geometry (pdf), Sov. Math. Dokl. 219:3 (1974) (with S.P.Novikov).

  94. Periodic and conditionally periodic analogs of the many-soliton solutions of the Korteweg - de Vries equation (pdf), Soviet Phys. JETP 67 (1974) 1058-1063 (with S.P.Novikov).

  95. Generalized Witt groups (pdf), Matem. Zametki 13:3 (1973) 419-426. English translation (pdf) in: Math. Notes 13:3 (1973) 253-257.