Институт теоретической физики им. Л.Д. Ландау


Российской академии наук

Петр Георгиевич Гриневич

Петр Георгиевич Гриневич

Старший научный сотрудник

Доктор физ.-мат. наук

Эл. почта:
Дом. страница: http://pgg.itp.ac.ru/
Skype: petr_grinevich_roma

Публикации

  1. S. Abenda, P.G. Grinevich, Periodic billiard orbits on n-dimensional ellipsoids with impacts on confocal quadrics and isoperiodic deformations, J. Geom. Phys., 60(10), 1617-1633 (2010); arXiv:0903.1980.
  2. П.Г. Гриневич, С.П. Новиков, Сингулярные конечнозонные операторы и индефинитные метрики, Успехи мат. наук, 64:4(388), 45–72 (2009) [G.Gr. Petrinevich, P.No. Sergeivikov, Singular finite-gap operators and indefinite metrics, Russ. Math. Surv., 64(4), 625-650 (2009)].
  3. П.Г. Гриневич, К.В. Кайпа, Многомасштабный предел конечнозонных решений уравнения sin-Гордона и вычисление топологического заряда с помощью тета-функциональных формул, Тр. МИАН, 266, 54–63 (2009) [P.G. Grinevich, K.V. Kaipa, Multiscale limit for finite-gap sine-Gordon solutions and calculation of topological charge using theta-functional formulae, Proc. Steklov Inst. Math., 266(1), 49-58 (2009)]; arXiv:0904.4520.
  4. P. Grinevich, S. Novikov, Singular Finite-Gap Operators and Indefinite Metric, arXiv:0903.3976.
  5. P.G. Grinevich, I.A. Taimanov, Spectral conservation laws for periodic nonlinear equations of the Melnikov type, Amer. Math. Soc. Transl. Ser. 2, Vol. 224, 125-138 (2008) [Geometry, Topology, and Mathematical Physics: S. P. Novikov's Seminar: 2006-2007. Edited by: V. M. Buchstaber and I. M. Krichever, ISBN-13: 978-0-8218-4674-2]; arXiv:0801.4143.
  6. P.G. Grinevich, K.V. Kaipa, Calculation of Topological Charge of Real Finite-Gap sine-Gordon solutions using Theta-functional formulae, arXiv:0812.2494.
  7. P.G. Grinevich, I.A. Taimanov, Infinitesimal Darboux Transformations of the Spectral Curves of Tori in the Four-Space, Int. Math. Res. Notices, 2007, rnm005 (2007) (21 pages); math/0611215.
  8. A. Doliwa, P. Grinevich, M. Nieszporski, P.M. Santini, Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme, J. Math. Phys., 48, 013513 (2007); nlin/0410046.
  9. P.G. Grinevich, P.M. Santini, Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve $\mu^2=\nu^n-1, n\in Z$: Ergodicity, isochrony, periodicity and fractals, Physica D 232 (1), 22-32 (2007); nlin/0607031.
  10. П.Г. Гриневич, Р.Г. Новиков, Ядро Коши для DN-дискретного комплексного анализа Новикова-Дынникова на треугольной решетке, Успехи мат. наук, 62:4(376), 155-156 (2007) [P.G. Grinevich, R.G. Novikov, The Cauchy kernel for the Novikov-Dynnikov DN-discrete complex analysis in triangular lattices, Russ. Math. Surv., 62(4), 799-801 (2007)].
  11. P.G. Grinevich, S.P. Novikov, Reality problems in the soliton theory, MSRI Publications, Vol. 55, 221-239 (2007) [Probability, Geometry and Integrable Systems. For Henry McKean's Seventy-Fifth Birthday. Ed. by M. Pinsky and B. Birnir. Cambridge University Press, Cambridge, 2007, x+324 pp. ISBN-13: 978-0-521-89527-9].
  12. P.G. Grinevich, $\bar\partial$ approach to integrable systems, Encyclopedia of Mathematical Physics, 34-41 (2006). eds. J.-P. Fransoise, G.L. Naber and Tsou S.T., Oxford: Elsevier, 2006.
  13. P.G. Grinevich, P.M. Santini, The initial boundary value problem on the segment for the Nonlinear Schrödinger equation; the algebro-geometric approach. I, Amer. Math. Soc. Transl. Ser. 2, Vol. 212, 157-178 (2004) [Geometry, Topology, and Mathematical Physics, Edited by: V. M. Buchstaber and I. M. Krichever, AMS, 2004; 324 pp; Advances in the Mathematical Sciences 55. ISBN: 0-8218-3613-7]; nlin/0307026.
  14. P.G. Grinevich, S.P. Novikov, Topological Charge of the real periodic finite-gap Sine-Gordon solutions, Commun. Pure Appl. Math., 56 (7), 956-978 (2003); math-ph/0111039.
  15. P.G. Grinevich, S.P. Novikov, Topological phenomena in the real periodic sine-Gordon theory, J. Math. Phys., 44 (8), 3174-3184 (2003); math-ph/0303039.
  16. P.G. Grinevich, Approximation theorem for the self-focusing Nonlinear Schrödinger Equation and for the periodic curves in R^3, Physica D 152-153, 20-27 (2001); nlin/0002020.
  17. П. Г. Гриневич, С. П. Новиков, Вещественные конечнозонные решения уравнения Sine-Gordon: формула для топологического заряда, Успехи мат. наук, 56:5(341), 181–182 (2001) [P.G. Grinevich, S.P. Novikov, Real finite-zone solutions of the sine-Gordon equation: a formula for the topological charge, Russ. Math. Surv., 56(5), 980–981 (2001)].
  18. П.Г. Гриневич, Преобразование рассеяния для двумерного оператора Шрёдингера с убывающим на бесконечности потенциалом при фиксированной ненулевой энергии, Успехи мат. наук, 55:6(336), 3–70 (2000) [P.G. Grinevich, Scattering transformation at fixed non-zero energy for the two-dimensional Schrodinger operator with potential decaying at infinity, Russ. Math. Surv., 55(6), 1015-1083 (2000)].
  19. P.G. Grinevich, M.U. Schmidt, Closed curves in R^3 and the nonlinear Schroedinger euation, Proc. the Workshop on Nonlinearity, Integrability and All That: Twenty years after NEEDS'79 (Galliopolu, 1999), World Scientific, p. 139-145 (2000).
  20. P.G. Grinevich, M.U. Schmidt, Conformal invariant functionals of tori into $R^3$, J. Geom. Phys., 26(1-2), 51-78 (1998); dg-ga/9702015.
  21. P.G. Grinevich, A.Yu. Orlov, Flag Spaces in KP Theory and Virasoro Action on \det D_j and Segal-Wilson \tau-Function, In: Research Reports in Physics. Problems of Modern Quantum Field Theory. Editors: A.A.Belavin, A.U.Klimyk, A.B.Zamolodchikov. Springer-Verlag Berlin, Heidelberg, 1989, pp. 86–106.; math-ph/9804019.
  22. P.G. Grinevich, R.G. Novikov, Discrete spectrum for n-cell potentials, Rapport de Recherche No 98/10-2, Universite de Nantes; math-ph/9811014.
  23. P.G. Grinevich, Nonsingularity of the direct scattering transform for the KP II equation with a real exponentially decaying-at-infinity potential, Lett. Math. Phys., 40 (1), 59-73 (1997); solv-int/9509010.
  24. P.G. Grinevich, M.U. Schmidt, Closed curves in R^3: a characterization in terms of curvature and torsion, the Hasimoto map and periodic solutions of the Filament Equation, dg-ga/9703020.
  25. P.G. Grinevich, R.G. Novikov, Transparent Potentials at Fixed Energy in Dimensoion Two. Fixed-Energy Dispersion Relations for the Fast Decaying Potentials, Commun. Math. Phys., 174 (2), 409-446 (1995); solv-int/9410003.
  26. P.G. Grinevich, M.U. Schmidt, Periodic preserving deformations of the finite-gap solutions of the soliton equations, Proc. 1st Worlshop «Nonlinear Physics. Theory and Experiment». Ed. E. Akfinito, M. Boiti, L. Martina, F. Pempinelli. World Scientific, 1996, p.124-130.
  27. P.G. Grinevich, R.G. Novikov, Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials, Commun. Math. Phys., 174, 409-446 (1995); solv-int/9410003.
  28. P.G. Grinevich, M.U. Schmidt, Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations, Physica D 87 (1-4), 73-98 (1995); solv-int/9412005.
  29. P.G. Grinevich, S.P. Novikov, Nonselfintersecting magnetic orbits on the plane. Proof of the overthrowing of cycles principle, Amer. Math. Soc. Transl. Ser. 2, Vol. 170, 57-82 (1995) [Topics in Topology and Mathematical Physics, Edited by: S. P. Novikov, 1995; 206 pp; ISBN-10: 0-8218-0455-3, SBN-13: 978-0-8218-0455-1]; solv-int/9501006.
  30. P.G. Grinevich, S.P. Novikov, Nonselfintersecting magnetic orbits on the plane. Proof of Principle of the Overthrowing of the Cycles, Amer. Math. Soc. Transl. series 2: Adv. Math. Sci., Vol. 170, 199-206 (1995); solv-int/9501006.
  31. П.Г. Гриневич, С.П. Новиков, Струнное уравнение – II. Физическое решение, Алгебра и анализ, 6(3), 118-140 (1994) [P.G. Grinevich, S.P. Novikov, String equation – 2. Physical solution, St. Petersburg Math. J., 6(3), 553-574 (1995)]; solv-int/9501002.
  32. P.G. Grinevich, Fast-decaying potentials on the finite-gap background and the ∂ˉ−problem on the Riemann surfaces, ТМФ, 99(2), 300–308 (1994) [Theor. Math. Phys., 99(2), 599-605 (1994)].
  33. P.G. Grinevich, Nonisospectral symmetries of the KdV equation and the corresponding symmetries of the Whitham equations, In: “Singular Limits of Dispersive Wawes” eds. N.M. Ercolany, I.R. Gabitov, C.D. Levermore, D.Serre, Plenum Press, NY, 1994, p.67-88 [NATO ASI Series, Ser. B: Physics, Vol. 320, Plenum, 1994]; solv-int/9509004.
  34. P.G. Grinevich, M.U. Schmidt, Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations, solv-int/9412005.
  35. V.A. Benderskii, D.E. Makarov, P.G. Grinevich, Quantum chemical dynamics in two dimensions, Chem. Phys., 170 (3), 275-293 (1993).
  36. P.G. Grinevich, A.Yu. Orlov, E.L. Schulman, On the symmetric of the Integrable Systems, In: Important developments in soliton theory, p.283-301 (1993). Ed. by Fokas A.S., Zakharov V.E. Berlin ea: Springer-Verlag, 1993, ix,559 pp. (Springer Ser. in Nonlinear Dynamics). ISBN 3-540-55913-2.
  37. P.G. Grinevich, The action of the Virasoro nonisospectral KdV symmetries of the Whitham equations, In: Nonlinear Precesses in Physics (Proc. of the 3 Potsdam — 5 Kiev Workshop at Clarkson Univ., Potsdam, NY, USA, Aug 1-11, 1991). Ed. A.S. Fokas, D.J. Kaup, A.C. Newell, V.E. Zakharov, Springer-Verlag, 1993, p.108-112.
  38. V.A. Benderskii, D.E. Makarov, D.L. Pastur, P.G. Grinevich, Preexponential factor of the rate constant of low-temperature chemical reactions. Fluctuational width of tunneling channels and stability frequencies, Chem. Phys., 161 (1-2), 51-61 (1992).
  39. П.Г. Гриневич, А.Ю. Орлов, Вариации комплексной структуры римановых поверхностей векторными полями на окружности и объекты теории КП. Задача Кричевера–Новикова о действии на функции Бейкера–Ахиезера, Функц. анализ и его прил., 24(1), 72–73 (1990) [P.G. Grinevich, A.Yu. Orlov, Variations of the complex structure of Riemann surfaces by vector fields on a contour and objects of the KP theory. The Krichever-Novikov problem of the action on the Baker-Akhieser functions, Funct. Anal. Appl., 24(1), 61-63 (1990)].
  40. P.G. Grinevich, A.Yu. Orlov, Higher (non-isospectral) symmetries of the Kadomtsev-Petviashvily equations and the Virasoro action on Riemann surfaces, In: Nonlinear Evolution Equations and Dynamical Systems. Ed. by S. Carillo, O. Ragnisco, Springer-Verlag, 1990, p.165-169.
  41. P.G. Grinevich, A.Y. Orlov, In: Problems of modern quantum field theory : Invited lectures of the Spring School, held in Alushta USSR, April 24-May 5, 1989. A.A. Belavin, A.U. Klimyk, A.B. Zamolodchikov, eds. Springer, 1990. ISBN: 0387518339.
  42. P.G. Grinevich, A.Yu. Orlov, Effect of additional symmetries of K-P equation on the finite-gap solutions and variations of Riemann surfaces. The Krichever-Novikov problem, In: Soliton and Applications (Proc. 4 Int. Workshop, Dubna, USSR, 24-26 Aug. 1989). Ed. V.G. Makhankov, V.K. Fedyanin, O.K. Pashaev, World Scientific, 1990, p.147-151.
  43. P.G. Grinevich, I.M. Krichever, Algebraic-geometry methods in soliton theory, In: Soliton theory: a survey of results, Chapter 14, p. 354-400. Ed. Allan P. Fordy, Manchester University Press, 1990, vii,449 pp. ISBN 9780719014918.
  44. П.Г. Гриневич, А.Ю. Орлов, Действие алгнбры Вирасоро на модулях римановых поверхностей. Реализация в теории уравнения Кадомцева-Петвиашвили. Задача Кричевера-Новикова л действии на функцию Бейкера-Ахиезера, В сб: Геометрия, тополоuия и приложения, Москва, 1990, с.100-105.
  45. П.Г. Гриневич, Быстроубывающие потенциалы на фоне конечнозонных и $\bar\partial$-проблема на римановых поверхностях, Функц. анализ и его прил., 23(4), 79–80 (1989) [P.G. Grinevich, Rapidly decreasing potentials on a background of finite-zone potentials and the [`(¶)]∂ˉ-problem on Riemann spaces, Funct. Anal. Appl., 23(4), 321-322 (1989)].
  46. P.G. Grinevich, A.Yu. Orlov, Virasoro action on Riemann surfaces, Grassmanians, det \bar\partial and Segal-Wilson \tau-function, In: Problems of modern quantum field theory (Invited lectures of the spring school held in Alushta, USSR, April 24 — May 5, 1989). Ed. A.A. Belavin, A.U. Klimyk, A.B. Zamolodchikov, Springer-Verlag, 1989, p. 86-106.
  47. P. Grinevich, G., A.Yu. Orlov, Wilson \teta-function and det \bar\partial, In: Nonlinear World: Proc. IV Int. Workshop on Nonlinear and Turbulent Processes in Physics, Kiev, 9-22 Oct. 1989. Ed. by A.G. Sitenko, V.E. Zakharov, V.M. Chernousenko. Kiev: Naukova Dumka, 1989, Vol.2, p.242-245.
  48. P. Grinevich, G., A.Yu. Orlov, Vector fields action on Riemann surfaces and KP theory. The Krichever-Novikov problem, In: Nonlinear World: Proc. IV Int. Workshop on Nonlinear and Turbulent Processes in Physics, Kiev, 9-22 Oct. 1989. Ed. by A.G. Sitenko, V.E. Zakharov, V.M. Chernousenko. Kiev: Naukova Dumka, 1989, Vol.2, p.246-249.
  49. P.G. Grinevich, G.E. Volovik, Topology of gap nodes in superfluid 3He: π4 Homotopy group for 3He-B disclination, J. Low Temp. Phys., 72 (5-6), 371-380 (1988).
  50. П. Г. Гриневич, С. П. Новиков, Двумерная «обратная задача рассеяния» для отрицательных энергий и обобщенно-аналитические функции. I. Энергии ниже основного состояния, Функц. анализ и его прил., 22(1), 23–33 (1988) [P.G. Grinevich, S.P. Novikov, Two-dimensional “inverse scattering problem” for negative energies and generalized-analytic functions. I. Energies below the ground state, Funct. Anal. Appl., 22(1), 19-27 (1988)].
  51. P.G. Grinevich, S.P. Novikov, Inverse scattering problem for the two-dimensional Schrodinger operator at a fixed negative energy and generalized analytic functions, Proc. 3 Int. Workshop on nonlinear and turbulent processes in physics, Kiev, 13-26 April 1987. Kiev, Naukova Dumka, 1988, p.86-89.
  52. P.G. Grinevich, S.P. Novikov, Two-dimensional «inverse scattering problem» for fixed negative energies and generalized analytic functions, Proc. of the «Plasma theory and nonlinear and turbulent processes in physics» Workshop, Kiev, 13-25 April 1987. World Scientific, 1988, p.58-85.
  53. S.V. Manakov, P. Grinevich, The inverse spectral problem for the two-dimensional Schroedinger operator, Physica D 28 (1-2), 222-222 (1987).
  54. П.Г. Гриневич, Р.Г. Новиков, Аналоги многосолитонных потенциалов для двумерного оператора Шредингера и нелокальная задача Римана, Докл. Акад. наук СССР, 286 (1), 19-22 (1986) [P.G. Grinevich, R.G. Novikov, Analogues of multisoliton potentials for the two-dimensional Schrodinger operator, and a nonlocal Riemann problem, Sov. Math., Dokl. 33(1), 9-12 (1986)].
  55. П.Г. Гриневич, Векторный ранг коммутирующих матричных дифференциальных операторов. Доказательство критерия С. П. Новикова, Изв. АН СССР, Сер. матем., 50(3), 458–478 (1986) [P.G. Grinevich, Vector rank of commuting matrix differential operators. Proof of S. P. Novikov's criterion, Math. USSR-Izv., 28(3), 445–465 (1987)].
  56. П.Г. Гриневич, Рациональные солитоны уравнений Веселова–Новикова – безотражательные при фиксированной энергии двумерные потенциалы, ТМФ, 69(2), 307-310 (1986) [P.G. Grinevich, Rational solitons of the Veselov-Novikov equations are reflectionless two-dimensional potentials at fixed energy, Theor. Math. Phys., 69(2), 1170-1172 (1986)].
  57. П.Г. Гриневич, С.В. Манаков, Обратная задача теории рассеяния для двумерного оператора Шрёдингера, $\bar\partial$-метод и нелинейные уравнения, Функц. анализ и его прил., 20(2), 14–24 (1986) [P.G. Grinevich, S.V. Manakov, Inverse scattering problem for the two-dimensional Schrödinger operator, the ∂ˉ-method and nonlinear equations, Funct. Anal. Appl., 20(2), 94-103 (1986)].
  58. П.Г. Гриневич, Коммутирующие матричные дифференциальные операторы произвольного ранга, Докл. Акад. наук СССР, 278 (5), 1048-1052 (1984) [P.G. Grinevich, Commuting differential operators of arbitrary rank, Sov. Phys. Dokl. 30(2), 515-518 (1984)].
  59. С. П. Новиков, П. Г. Гриневич, О спектральной теории коммутирующих операторов ранга 2 с периодическими коэффициентами, Функц. анализ и его прил., 16(1), 25–26 (1982) [S.P. Novikov, P.G. Grinevich, Spectral theory of commuting operators of rank two with periodic coefficients, Funct. Anal. Appl., 16(1), 19-20 (1982)].