Boris Dubrovin Publications

List of Papers of Boris Dubrovin

  1. Generalized Witt groups. Math. Notes (1973).

  2. Inverse problem of scattering theory for periodic finite-zone potentials. Functional. Anal. Appl. 9:1 (1975).

  3. Periodic problem for the Korteweg -- de Vries equation in the class of finite-zone potentials. Functional. Anal. Appl. 9:3 (1975), 41-51.

  4. Periodic Korteweg -- de Vries and Sturm -- Liouville problems. Their relation to algebraic geometry. Sov. Math. Dokl. 219:3 (1974) (with S.P.Novikov).

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

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

  7. Non-linear equations of Korteweg -- de Vries type, finite-zone linear operators, and Abelian varieties. Russian Math. Surv. 31:1 (1976), 55-136 (with V.B.Matveev and S.P.Novikov).

  8. Finite-zone linear differential operators and Abelian varieties. Russian Math. Surv. 31:4 (1976).

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

  10. Completely integrable Hamiltonian systems, associated with matrix operators, and Abelian varities. Funct. Anal. Appl. 11:4 (1977).

  11. Geometry of Riemann surfaces and nonlinear differential equations. Russian Math. Surv. 32:1 (1977) (with I.M.Krichever).

  12. 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).

  13. Ground states of two-dimensional electron in periodic magnetic field. Soviet JETP 79:3 (1980) (with S.P.Novikov).

  14. Ground states of electron in magnetic field. Russian Math. Surv. 35:5 (1980) (with S.P.Novikov).

  15. Ground states in magnetic field, magnetic Bloch functions and vector bundles. Soviet Math. Dokl. 253:6 (1980) (with S.P.Novikov).

  16. Multidimensional theta-functions and their applications to solving of differential equations. Russian Math. Surv. 36:3 (1981).

  17. Theta-functions and nonlinear equations. Russian Math. Surv. 36:2 (1981), 11-80.

  18. The Kadomtsev -- Petviashvili equation and relations for the periods of holomorphic differentials on Riemann surfaces. Math. USSR Izvestia 45:5 (1981).

  19. Applications of nonlinear equations to classical problems of geometry of Riemann surfaces. Russian Math. Surv. 36:4 (1981).

  20. On approximation of real periodic solutions of the Sine-Gordon equation by finite-gap solutions. Russian Math. Surv. 37:4 (1982).

  21. Real two-gap solutions of the Sine-Gordon equation. Funct. Anal. Appl. 16:1 (1982), 27-43 (with S.M.Natanzon).

  22. 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.

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

  24. 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).

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

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

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

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

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

  30. Integrable systems. I. 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.

  31. 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).

  32. Real theta-functional solutions of the Kadomtsev-Petviashvili equation. Math. USSR Izvestia 52:2 (1988) (with S.M.Natanzon).

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

  34. Differential-geometric Poisson brackets on a lattice. Funct. Anal. Appl. 23:2 (1989), 57-59.

  35. Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory. Russian Math. Surv. 44:6 (1989), 29-98 (with S.P.Novikov).

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

  37. On differential geometry of strongly integrable systems of hydrodynamic type. Funct. Anal. Appl. 24:4 (1990).

  38. Weakly perturbed soliton lattices. Nucl. Phys. B (Proc. Suppl.) 18A (1990), 23.

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

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

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

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

  43. Integrable systems and classification of 2D topological field theories. 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. Birkh\"auser, 1993.

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

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

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

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

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

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

  50. Geometry of 2D topological field theories. 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., vol. 1620 (1996), pp. 120 - 348.

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

  52. Functionals of the Peierls - Froehlich Type and the Variational Principle for the Whitham Equations. In: Amer. Math. Soc. Transl. (2) Vol. 179 (1997) 35-44.

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

  54. Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation (with Youjin Zhang), hep-th/9712232, Comm. Math. Phys. 198 (1998) 311-361.

  55. Flat pencils of metrics and Frobenius manifolds math.DG/9803106, Proceedings of 1997 Taniguchi Symposium "Integrable Systems and Algebraic Geometry", Editors M.-H. Saito, Y.Shimizu and K.Ueno, 47-72. World Scientific, 1998.

  56. Painleve' transcendents and topological field theory In: "The Painleve' property: one century later", R.Conte (Ed.), Springer Verlag, 1999, p.287-412.

  57. Monodromy of certain Painleve'-VI transcendents and reflection groups (with M.Mazzocco), math.AG/9806056, Inventiones Math. 141 (2000) 55-147.

  58. Geometry and analytic theory of Frobenius manifolds 11 pages, math/9807034, Proceedings of ICM98, Vol. 2, 315-326.

  59. Frobenius manifolds and Virasoro constraints (with Youjin Zhang), math/9808048, Selecta Mathematica 5 (1999) 423-466.

  60. The Extended Toda Hierarchy (with Guido Carlet and Youjin Zhang), nlin.SI/0306060, Moscow Math. J. 4 (2004) 313-332.

  61. On almost duality for Frobenius manifolds, math.DG/0307374, Amer. Math. Soc. Transl. 212(2004) 75-132.

  62. Virasoro Symmetries of the Extended Toda Hierarchy (with Youjin Zhang), math.DG/0308152, Comm. Math. Phys. 250 (2004) 161-193.

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

  64. On analytic families of invariant tori for PDEs, Asterisque 297 (2004) 35-65.

  65. On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasi-triviality of bi-hamiltonian perturbations (with Si-Qi Liu, Youjin Zhang), math.DG/0410027, Comm. in Pure Appl. Math. 59 (2006) 559 - 615.

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

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

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

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

  70. On universality of critical behaviour in the focusing nonlinear Schroedinger equation, elliptic umbilic catastrophe and the tritronquee solution to the Painleve'-I equation (with T.Grava and C.Klein), arXiv:0704.0501 (32 pages)

  71. Frobenius manifolds and central invariants for the Drinfeld - Sokolov bihamiltonian structures (with Si-Qi Liu, Youjin Zhang), arXiv:0710.3115 (73 pages)