P.G.Grinevich:


List of publications

  1. Grinevich P.G., Mironov A.E., Novikov S.P. "2D Schrodinger Operator, (2+1) Systems and New Reductions. The 2D Burgers Hierarchy and Inverse Problem Data" - Avaliable at the arxiv.org/archive/math arXiv:1005.0612 e-Print archive: Tex file | Ps file | Pdf file
  2. Grinevich P.G., Mironov A.E., Novikov S.P. "On the zero level of purely magnetic nonrelativistic 2D Pauli Operators (spin=1/2)" - Avaliable at the arxiv.org/archive/math arXiv:1004.1157 e-Print archive: Tex file | Ps file | Pdf file
  3. Grinevich P.G., Mironov A.E., Novikov S.P. "New Reductions and Nonlinear Systems for 2D Schrodinger Operators" - Avaliable at the arxiv.org/archive/math arXiv:1001.4300 e-Print archive: Tex file | Ps file | Pdf file
  4. Abenda S., Grinevich P. "Periodic billiard orbits on n-dimensional ellipsoids with impacts on confocal quadrics and isoperiodic deformations " - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  5. Grinevich P.G., Novikov S.P. "Singular Finite-Gap Operators and Indefinite Metric. I" -- Uspekhi. Mat. Nauk, 2009, v. 64, №4, pp. 45-72 (in Russian); English translation -- to appear in: Russian Mathematical Surveys, 2009, v. 64, No 4, pp. - ; Isaac Newton Institute for Mathematical Sciences preprint NI09030-DIS - Avaliable at the arxiv.org/archive/math e-Print archive: Tex file | Ps file | Pdf file
  6. Grinevich P.G, Kaipa K. "Calculation of Topological Charge of Real Finite-Gap sine-Gordon solutions using Theta-functional formulae" -- Trudy Matematicheskogo Instituta imeni V.A.Steklova, 2009, v. 266, pp. 54-63 (in Russian); English translation: Proceedings of the Steklov Institute of Mathematics, 2009, v. 266, pp. 49-58. - Avaliable at the arxiv.org/archive/math e-Print archive: Tex file | Ps file | Pdf file
  7. Grinevich P.G, Taimanov I.A. "Spectral conservation laws for periodic nonlinear equations of the Melnikov type." - Amer. Math. Soc. Transl. Ser. 2, 2008, v. 224, pp. 125-138; Max-Plank-Institute für Mathematik preprint MPI 08-10 - Avaliable at the arxiv.org/archive/math e-Print archive: Tex file | Ps file | Pdf file
  8. Grinevich P.G., Novikov S.P. "Reality problems in the soliton theory." - Probability, Geometry and Integrable Systems. MSRI Publications Volume 55, 2007, pp. 221-239. - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  9. Grinevich P.G., Novikov R.G. "The Cauchy kernel for the Novikov--Dynnikov DN-discrete complex analysis in triangular lattices."-- Uspekhi. Mat. Nauk, 2007, v. 62, №4, pp. 155-156 (in Russian); English translation: Russian Mathematical Surveys, 2007, v. 62, No 4, pp. 799-801.
  10. Grinevich P.G, Taimanov I.A. "Infinitesimal Darboux transformations of the spectral curves of tori in the four-space" - Int Math Res Notices, 2007, v. 2007, article ID rnm005, 21 pages, published on May 24, 2007 - Avaliable at the arxiv.org/archive/math e-Print archive: Tex file | Ps file | Pdf file
  11. Grinevich P.G, Santini P.M. "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: Nonlinear Phenomena, 2007, v. 232, Issue 1, pp. 22-32. - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  12. Doliwa A., Grinevich P.G., Nieszporski M., Santini P.M. "Integrable lattices and their sub-lattices: from the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme." - Journal of Mathematical Physics, 2007, v.48. No.1. 28 pages. - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  13. Grinevich P.G. "&part -bar approach to integrable systems." - Encyclopedia of Mathematical Physics, eds. J.-P. Fransoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. pp 34--41.
  14. Grinevich P.G, Santini P.M. "The initial boundary value problem on the interval for the Nonlinear Schrodinger equation; the algebro-geometric approach. I." - American Mathematical Society Translations - Series 2, Advances in the Mathematical Sciences, 2004, v. 212., pp. 157-178. - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  15. Grinevich P.G., Novikov S.P. "Topological phenomena in the real periodic sine-Gordon theory." - Journal of Mathematical Physics, 2003, v.44, Issue 8, pp. 3174-3184. - Avaliable at the arxiv.org/archive/math-ph e-Print archive: Tex file | Ps file | Pdf file
  16. Grinevich P.G., Novikov S.P. "Topological charge of the real periodic finite-gap Sine-Gordon solutions." - Communications on Pure and Applied Mathematics, 2003, v.56, Issue 7, pp. 956-978. - Avaliable at the arxiv.org/archive/math-ph e-Print archive: Tex file | Ps file | Pdf file
  17. Grinevich P.G., Novikov, S.P. "Real finite-gap Sine-Gordon solutions: a formula for topological charge." - Uspekhi. Mat. Nauk, 2001, v. 56, №5, pp. 181--182 (in Russian); English translation: Russ. Math. Surveys, 2001, v. 56, №5, pp. 980--981.
  18. Grinevich P.G. "Approximation theorem for the self-focusing nonlinear Schrodinger equation and for the periodic curves in R 3." - Advances in nonlinear mathematics and science - Phys. D, 2001, v. 152/153, pp. 20--27. - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  19. Grinevich, P.G. Schmidt, M.U. "Closed curves in R3 and the nonlinear Schrodinger equation." - Proceedings of the Workshop on Nonlinearity, Integrability and All That: Twenty Years after NEEDS '79 (Gallipoli, 1999), pp. 139-145, World Sci. Publishing, River Edge, NJ, 2000.
  20. Grinevich P.G. "The scattering transform for the two-dimensional Schrodinger operator with a potential that decreases at infinity at fixed nonzero energy." - Uspekhi Mat. Nauk, 2000, v. 55, №6(336), pp. 3--70 (in Russian); English translation: Russian Math. Surveys, 2000, v. 55, №6, pp. 1015--1083.
  21. Grinevich P.G, Novikov R.G. "Discrete spectrum for n-cell potentials." - Rapport de Recherche №98/10-2, Universite de Nantes; - Avaliable at the arxiv.org/archive/math-ph e-Print archive: Tex file Ps file Pdf file
  22. Grinevich P.G. "Complex manifold", "Conformal transformation", "Holomorphic form", "Holomorphic map". -- Mathematical physics. Encyclopedia. (in Russian). Editor-in-chief -- L.D.Faddeev. 1998.
  23. Grinevich P.G., Schmidt M.U. "Conformal invariant functionals of immersions of tori into R 3." - Journal of Geometry and Physics, 1998, v. 26, №1-2, pp. 51-78; SFB 288 preprint №252, Berlin, Feb 1997; - Avaliable at the arxiv.org/archive/math.DG e-Print archive: Tex file | Ps file | Pdf file
  24. Grinevich P.G., Schmidt M.U. "Closed curves in R3: a characterization in terms of curvature and torsion, the Hasimoto map and periodic solutions of the Filament Equation." - SFB 288 preprint №254; - Avaliable at the arxiv.org/archive/math.DG e-Print archive: Tex file | Ps file | Pdf file
  25. Grinevich P.G. "Nonsingularity of the direct scattering transform for the Kadomtsev-Petviashvili 2 equation with real exponentially decaying at infinity potential." - Lett. Math. Phys., 1997, v. 40, pp. 59-73; Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  26. Grinevich P.G., Schmidt M.U. "Periodic preserving deformations of the finite-gap solutions of the soliton equations." in: Proceedings of the first workshop "Nonlinear physics. Theory and experiment". editors: E.Alfinito, M.Boiti, L.Martina, F.Pempinelli. World Scientific (1996). pp. 124-130.
  27. Grinevich P.G., Novikov R.G. "Transparent Potentials at Fixed Energy in Dimension Two. Fixed-Energy Dispersion Relations for the Fast Decaying Potentials." - Commun. Math. Phys., 1995, v.174, pp. 409-446. - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file
  28. Grinevich P.G., Novikov S.P. "Nonselfintersecting magnetic orbits on the plane. Proof of Principle of the Overthrowing of the Cycles." - Translations of American Mathematical Society, series 2., 1995, v.170, pp. 59-82; - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  29. Grinevich P.G., Schmidt M.U. "Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations." - Physica D, 1995, v. 87, pp 73-98; SFB 288 preprint №150, Berlin, Dec 1994; - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  30. Grinevich P.G. "Nonisospectral symmetries of the KdV equation and the corresponding symmetries of the Whitham equations." - In "Singular limits of Dispersive waves", ed. N.M.Ercolany, I.R.Gabitov, C.D.Levermore, D.Serre, NATO ASI Series, Series B: Physics Vol. 320, Plenum, 1994, pp. 67-88. - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  31. P.G.Grinevich. "Fast decaying potentials on the finite-gap background and the $\bar\partial$-problem on the Riemann surfaces." - Teoreticheskaya i Mathematicheskaya Fizika, 1994, v. 99, №2, pp. 300-308; Theor. Math. Phys., 1994, v.99, pp. 599-605.
  32. Grinevich P.G., Novikov S.P. "String equation-2. Physical solution." --Algebra and Analysis, 1994, v.6, №3, pp. 118-140 (in Russian); English translation: St. Petersburg Math. J., 1995, v. 6, №3, pp. 553-574. - Avaliable at the arxiv.org/archive/nlin e-Print archive: Tex file | Ps file | Pdf file
  33. Grinevich P.G. "The action of the Virasoro nonisospectral KdV symmetries of the Whitham equations." - in "Nonlinear Processes in Physics" (Proccedings of the 3 Potsdam - 5 Kiev Workshop at Clarkson University, Potsdam, NY, USA, August 1-11, 1991), ed. A.S.Fokas, D.J.Kaup, A.C.Newell, V.E.Zakharov, Springer-Verlag, 1993, pp. 108-112.
  34. Grinevich P.G., Orlov A.Yu, Schulman E.I. "On the symmetries of the integrable systems." - In the book. "Important developments in soliton theory", ed. A. Fokas, V.E. Zakharov, Springer-Verlag, Berlin - Heidelberg - New York, 1993, pp. 283-301.
  35. Benderskii V.A., Grinevich P.G., Makarov D.E. "Quantum chemical dynamics in two dimensions." - Chem. Phys., 1993, v. 170, pp. 275-293.
  36. Benderskii V.A., Grinevich P.G., Makarov D.E., Pastur D.L. "Preexponential factor of rate constant of low-temperature chemical reactions. Fluctuational width of tunneling channels and stability frequences." - Chem. Phys., 1992, v.161, pp. 51-61.
  37. Grinevich P.G., Orlov A.Yu. "Virasoro algebra action on the moduli of Riemann surfaces. Realization in the Kadomtsev-Petviashvily equation theory. The Krichever-Novikov problem about the action on the Baker-Akhieser function." - In "Geometry and topology and applications", Moscow, 1990 pp. 100-104, (in Russian).
  38. Grinevich P.G., Orlov A.Yu. "Higher (non-isospectral) symmetries of the Kadomtsev-Petviashvily equations and the Virasoro action on Riemann surfsces." - In "Nonlinear evolution equations and dynamical systems", ed. S.Carillo, O.Ragnisco, Springer-Verlag, 1990, pp 165-169.
  39. Grinevich P.G., Orlov A.Yu. "Effect of additional symmetries of K-P equation on the finite-gap solutions and variatons of Riemann surfaces. The Krichever-Novikov problem." - In "Soliton and applications" (Proceedings of the 4 international Workshop, Dubna, USSR, 24 - 26 August 1989), ed. V.G.Makhankov, V.K.Fedyanin, O.K.Pashaev, World Scientific 1990, pp. 147-151.
  40. Grinevich P.G., Krichever I.M. "Algebraic-geometry methods in soliton theory." - In "Soliton theory: a survey of results", ed. A.Fordy, University press, 1990, pp. 354-400.
  41. Grinevich P.G., Orlov A.Yu. "Variations of the complex structures of the Riemann surfaces by the vector fields in the circle and the KP theory objects. The Krichever-Novikov problem of the action on the Baker-Akhiezer function." - Funct. Anal. i ego Pril., 1990, v.24, №1, pp. 72-73 (in Russian); English translation: Funct. Anal. Appl. 1990, v. 24, pp.61-64.
  42. Grinevich P.G., Orlov A.Yu. "Virasoro action on Riemann surfaces, Grassmanians, det d-bar and Segal-Wilson tau - function." - In Problems of modern quantum field theory (Invited lecvtures 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, pp. 86-106. - The first version of this text is avaliable at the arxiv.org/archive/math-ph e-Print archive: Tex file | Ps file | Pdf file
  43. Grinevich P.G., Orlov A.Yu. Wilson tau - function and det d-bar." - In Nonlinear world: Proceedings of the 4 international workshop on nonlinear and turbulent processes in physics. Kiev 9-22 Oktober, 1989, Kiev, Naukova Dumka 1989,v. 2, pp.242-245.
  44. Grinevich P.G., Orlov A.Yu. "Vector fields action on Riemann surfaces and KP theory. The Krichever-Novikov problem." - In Nonlinear world: Proceedings of the 4 international workshop on nonlinear and turbulent processes in physics.Kiev 9-22 Oktober, 1989, Kiev, Naukova Dumka 1989, v. 2, pp.246-249.
  45. Grinevich P.G. "Fast decreasing potentials on a background of finite-zone potential and the d-bar - problem on Riemann spaces." - Funct. Anal. i ego Pril., 1989, v. 23, №4, pp. 79-80 (in Russian); English translation: Funct. Anal. Appl. 1989, v. 23, pp. 321-322.
  46. Grinevich P.G., Novikov S.P. "Inverse scattering problem for the two-dimensional Schrodinger operator at a fixed negative energy and generalized analytic functions." - Proceedings of the 3 international workshop on nonlinear and turbulent processes in physics.Kiev 13-26 April, 1987, Kiev, Naukova Dumka 1988, pp. 86-89.
  47. Grinevich P.G., Novikov S.P. "Two-dimensional 'inverse scattering problem' for fixed negative energies and generalized analytic functions." - In Proc. of the "Plasma theory and nonlinear and turbulent processes in physics" Workshop, Kiev 13-25 April 1987. World Scientific 1988, pp. 58-85.
  48. Grinevich P.G., Volovik G.E. "Topology of gap nodes in superfluid 3He: pi4 homotopy group for 3 He-B disclination." - Journal of Low Temp. Phys. 1988, v.72, Nos 5/6, 371-380.
  49. Grinevich P.G., Novikov S.P. "Two-dimensional 'inverse scattering problem' for negative energies and generalized-analytic functions. 1. Energies below the ground state." - Funct. Anal. i ego Pril., 1988, v. 22, №1, pp. 23-33 (in Russian); Funct.Anal.Appl., 1988, v. 22, pp. 19-27.
  50. Grinevich P.G. "Rational solitons of the Veselov-Novikov equations are potential reflectionless at fixed energy." - Teoreticheskaya i Mathematicheskaya Fizika, 1986, v.69, №2, pp. 307-310 (in Russian); English translation: Theor. Math. Phys. 1986, v.69, pp. 1170-1172.
  51. Grinevich P.G. "Vector rank of commuting matrix differential operators. Proof of the S.P.Novikov criterion." - Izvestiia. AN SSSR, 1986, v.50, №3, pp. 458-478 (in Russian); English translation: Mathematics of the USSR, Izvestiya, 1987, v. 28, №3, pp. 445-465.
  52. Grinevich P.G. Manakov S.V. "Inverse scattering problem for the two-dimensional Schrodinger operator, d-bar - method and nonlinear equations." - Funct. Anal. i ego Pril., 1986, v. 20, №1, pp. 14-24 (in Russian); English translation: Funct. Anal. Appl., 1986, v.20, pp. 94-103.
  53. Grinevich P.G., Novikov R.G. "Analogues of multisoliton potentials for the two-dimensional Schrodinger operator, and a nonlocal Riemann problem." - Dokl. Akad. Nauk SSSR, 1986, v.286, №1, pp. 19-22 (in Russian). English translation: Soviet Math. Dokl. 1986, v.33, №1, pp. 9-12.
  54. Grinevich P.G., Novikov R.G. "Analogues of multisoliton potentials for the two-dimensional Schrodinger operator." - Funct. Anal. i ego Pril., 1985, v. 19, №4, pp. 32-42(in Russian); English translation: Funct.Anal.Appl., 1985, v.19, pp. 276-285.
  55. Grinevich P.G. "Commuting matrix differential orerators of arbitrary rank." - Dokl. Akad. Nauk SSSR, 1984, v.278,№5, pp. 1048-1052. English translation: Soviet Math. Dokl. 1984, v.30, №2, pp. 515-518.
  56. Novikov S.P., Grinevich P.G. "About the spectral theory of commuting operators of rank 2 with periodic coefficients." - Funct. Anal. i ego Pril., 1982, v. 16, №1, pp. 25-26 (in Russian); English translation: Funct. Anal. Appl., 1982, v. 16, pp. 19-21.
  57. Grinevich P.G. "Rational solutions for the equations of commutation of differential operators." - Funct. Anal. i ego Pril., 1982, v.16, №1, pp. 19-24 (in Russian); English translation: Funct. Anal. Appl., 1982, v. 16, pp. 15-19.

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