P.G.Grinevich:


List of publications

  1. Grinevich P.G., Novikov R.G. "Transparent scatterers and transmission eigenvalues"; - Available at the at the hal archive: hal-04682848, version 1; and arxiv.org/archive/math-ph arXiv: 2407.16451 e-Print archive: Abstract | Tex file | Pdf file
  2. Grinevich P.G. "Riemann Surfaces Close to Degenerate Ones in the Theory of Rogue Waves" - Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, v. 525, №6(468), pp. 93-118 (in Russian); doi:10.4213/tm4390; English translation: "Riemann Surfaces Close to Degenerate Ones in the Theory of Rogue Waves" - Proc. Steklov Inst. Math., v. 325 (2024), pp. 86-110; Online access; doi:10.1134/S0081543824020056;
  3. Coppini F., Grinevich P.G., Santini P.M. "The periodic N breather anomalous wave solution of the Davey-Stewartson equations; first appearance, recurrence, and blow up properties" - J. Phys. A, v. 57 (2024), 15208 , 27 pp., doi:10.1088/1751-8121/ad107b; Available at the arxiv.org/archive/nlin arXiv: 2308.12422 e-Print archive: Abstract | Tex file | Pdf file
  4. Grinevich P.G., Santini P.M. "The finite gap method and the periodic Cauchy problem of 2+1 dimensional anomalous waves for the focusing Davey-Stewartson 2 equation" - Uspekhi Mathematicheskich Nauk, 2022, v. 77, №6(468), pp. 77-107 (in Russian); doi:10.4213/rm10077; English translation: "The finite-gap method and the periodic Cauchy problem for (2+1)-dimensional anomalous waves for the focusing Davey-Stewartson 2 equation" - Russian Math. Surveys, v. 77 №6 (2022), pp. 1029-1059; doi:10.4213/rm10077e; - Available at the arxiv.org/archive/math-ph arXiv:2206.11950 e-Print archive: Abstract | Tex file | Pdf file
  5. Grinevich P.G., Novikov R.G. "Spectral inequality for the Schrodinger operator with a multipoint potential" - Uspekhi Mathematicheskich Nauk, 2022, v. 77, №6(468), pp. 69-76 (in Russian); doi:10.4213/rm10080; English translation: Grinevich P.G., Novikov R.G. "Spectral inequality for Schrodinger's equation with multipoint potential" - Russian Math. Surveys, v.77 6 (2022), №6 (2022), pp. 1021--1028 doi:10.4213/rm10080e;
  6. Bolsinov A.V., Buchstaber V.M., Veselov A.P., Grinevich P.G., Dynnikov I.A., Kozlov V.V., Kordyukov Yu.A.,Millionshchikov D.V., Mironov A.E., Novikov R.G., Novikov S.P., Yakovlev A.A., "Iskander Asanovich Taimanov (on his 60th birthday)" - Uspekhi Mathematicheskich Nauk, 2022, v. 77, №6(468), pp. 209-218 (in Russian); doi:10.4213/rm10091;
  7. Abenda S., Grinevich P.G. "Real regular KP divisors on M-curves and totally non-negative Grassmannians" - Letters in Mathematical Physics, 2022, v. 112, 115 (Published online), 64 pages; Article link (open access)
  8. Abenda S., Grinevich P.G. "Geometric Nature of Relations on Plabic Graphs and Totally Non-negative Grassmannians" - Int Math Res Notices, 2022, article ID rnac162, published on July 8, 2022, 66 pages; Article link; doi:10.1093/imrn/rnac162; - Available at the arxiv.org/archive/math.CO arXiv:2111.05782 e-Print archive: Abstract | Tex file | Pdf file
  9. Abenda S., Grinevich P.G. "Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians" - Advances in Mathematics, 2022, v. 406, 108523; doi:10.1016/j.aim.2022.108523; - Available at the arxiv.org/archive/math.CO arXiv:1908.07437 e-Print archive: Abstract | Tex file | Pdf file
  10. Coppini F., Grinevich P.G., Santini P.M. "Periodic rogue waves and perturbation theory", Encyclopedia of Complexity and Systems Science, 2022, eds. R. A. Meyers, Springer Science+Business Media LLC, 22 pages; Published online: https://link.springer.com/referenceworkentry/10.1007/978-3-642-27737-5_762-2; doi:10.1007/978-1-0716-2621-4_762;
  11. Grinevich P.G., Novikov R.G. "Transmission eigenvalues for multipoint scatterers" - Eurasian Journal of Mathematical and Computer Applications, 2021, Volume 9, Issue 4, pp. 17-25; - Available at the at the hal archive: hal-03326122, version 1; and arxiv.org/archive/math-ph arXiv:arXiv:2108.08361 e-Print archive: Abstract | Tex file | Pdf file
  12. Grinevich P.G., Santini P.M. "The linear and nonlinear instability of the Akhmediev breather" - Nonlinearity, 2021, v.34, pp. 8331-8358; doi:10.1088/1361-6544/ac3143; - The first version of the text (it was essentially modified during the review process) is available at the arxiv.org/archive/nlin.PS arXiv:2011.11402 e-Print archive: Abstract | Tex file | Pdf file
  13. Buchstaber V.M., Varchenko A.N., Veselov A.P., Grinevich P.G., Grushevsky S., Dobrokhotov S.Yu., Zabrodin A.V., Marshakov A.V, Mironov A.E., Nekrasov N.A., Novikov S.P., Okounkov A.Yu., Olshanetsky M.A., Pogrebkov A.K., Taimanov I.A., Tsfasman M.A., Chekhov L.O., Sheinman O.K., Shlosman S.B. "Igor Moiseevich Krichever (on his 70th birthday)" - Uspekhi Mathematicheskich Nauk, 2021, v. 76, No. 4(460), pp. 183-191 (in Russian); doi:10.4213/rm10015; English translation - Russian Mathematical Surveys, 2021, v.76, No. 4; doi:10.1070/RM10015
  14. Abenda S., Grinevich P.G. "A generalization of Talaska formula for edge vectors on plabic networks in the disk" - Available at the arxiv.org/archive/math.CO arXiv:2108.03229 e-Print archive: Abstract | Tex file | Pdf file
  15. Abenda S., Grinevich P.G. "Real regular KP divisors on M-curves and totally non-negative Grassmannians " - Available at the arxiv.org/archive/math-ph arXiv:2002.04865 e-Print archive: Abstract | Tex file | Pdf file
  16. Coppini F., Grinevich P.G., Santini P.M. "The effect of a small loss or gain in the periodic NLS anomalous wave dynamics. I" - Phys. Rev. E, 2020, v.101, No 3, 032204, 8 pages, - Published 6 March 2020; doi:10.1103/PhysRevE.101.032204; - Available at the arxiv.org/archive/nlin arXiv:1910.13176 e-Print archive: Abstract | Tex file | Pdf file
  17. Grinevich P.G., Novikov R.G. "Creation and annihilation of point-potentials using Moutard-type transform in spectral variable" - Journal of Mathematical Physics, 2020, v. 61, 093501, 7 pages, Published 6 March 2020; Published Online: 01 September 2020; doi:10.1063/1.5143303; - Available at the arxiv.org/archive/math.CV arXiv:1911.09627 e-Print archive: Abstract | Tex file | Pdf file
  18. Abenda S., Grinevich P.G. "Reducible M-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons" - Selecta Mathematica, 2019, v. 25:43, doi:/10.1007/s00029-019-0488-5; - Available at the arxiv.org/archive/math-ph arXiv:1805.05641 e-Print archive: Abstract | Tex file | Pdf file
  19. Grinevich P.G., Novikov R.G. "Moutard transform for the two-dimensional conductivity equation" - Letters in Mathematical Physics, 2019, v. 109, pp. 2209-2222; doi:/10.1007/s11005-019-01183-x; - Available at the hal archive: hal-01673778; and arxiv.org/archive/math-ph arXiv:1801.00295 e-Print archive: Abstract | Tex file | Pdf file
  20. Pierangeli D., Flammini M., Zhang L., Marcucci G., Agranat A.J., Grinevich P.G., Santini P.M., Conti C., DelRe E. "Observation of Fermi-Fasta-Flam-Tsingou recurrence in optical experiment" - Journal of Oceanological Research - 2019, v. 47, No. 1, p. 107 (Russian), p.108 (English); doi:10.29006/1564-2291.JOR-2019.47(1).32 ;
  21. Grinevich P.G., Santini P.M. "The finite gap method and the periodic NLS Cauchy problem of the anomalous waves, for a finite number of unstable modes" - Uspekhi Mathematicheskich Nauk, 2019, v. 74, No. 2(446), pp. 27-80 (in Russian); doi:10.4213/rm9863; English translation - Russian Mathematical Surveys, 2019, v.74, No. 2, pp. 211-263; doi:10.1070/RM9863; - Available at the ar - Available at the arxiv.org/archive/math-ph arXiv:1810.09247 e-Print archive: Abstract | Tex file | Pdf file
  22. Grinevich P.G., Santini P.M. "Numerical instability of the Akhmediev breather and a finite-gap model of it" - In "Recent Developments in Integrable Systems and Related Topics of Mathematical Physics (Kezenoi-Am, Russia, 2016)", ed. Viktor M. Buchstaber, Sotiris Konstantinou-Rizos, Alexander V. Mikhailov, Springer Proceedings in Mathematics & Statistics, v. 273, Springer 2019, pp. 3-23; doi:10.1007/978-3-030-04807-5_2; - Available at the arxiv.org/archive/nlin.PS arXiv:1708.00762 e-Print archive: Abstract | Tex file | Pdf file
  23. Abenda S., Grinevich P.G. "Real soliton lattices of KP-II and desingularization of spectral curves: the GrTP (2,4) case" - Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, v. 302, pp. 7-22 (in Russian); doi:10.1134/S0371968518030019; English translation: Proc. Steklov Inst. Math., 2018, v. 302, pp. 1-15; doi:10.1134/S0081543818060019; - Available at the arxiv.org/archive/math-ph arXiv:1803.10968 e-Print archive: Abstract | Tex file | Pdf file
  24. Pierangeli D., Flammini M., Zhang L., Marcucci G., Agranat A.J., Grinevich P.G., Santini P.M., Conti C., DelRe E. "Observation of Fermi-Pasta-Ulam-Tsingou recurrence and its exact dynamics" - Physical Review X, 2018, v. 8, issue 4, p. 041017 (9 pages); doi:10.1103/PhysRevX.8.041017;
  25. Grinevich P.G., Santini P.M. "The finite gap method and the analytic description of the exact rogue wave recurrence in the periodic NLS Cauchy problem. 1" - Nonlinearity, 2018, v. 31, No. 11, pp. 5258--5308; doi:10.1088/1361-6544/aaddcf; - Available at the arxiv.org/archive/nlin.SI arXiv:1707.05659 e-Print archive: Abstract | Tex file | Pdf file
  26. Grinevich P.G., Santini P.M. "Phase resonances of the NLS rogue wave recurrence in the quasi-symmetric case" - Theoretical and Mathematical Physics, 2018, v. 196, №3, pp. 404-418 (in Russian); doi:10.4213/tmf9544; English translation: Theoretical and Mathematical Physics, 2018, v. 196:3, pp. 1294-1306; doi:10.1134/S0040577918090040;
  27. Abenda S., Grinevich P.G. "KP theory, plane-bipartite networks in the disk and rational degenerations of M-curves" - Available at the arxiv.org/archive/math-ph arXiv:1801.00208 e-Print archive: Abstract | Tex file | Pdf file
  28. Abenda S., Grinevich P. "Rational degeneration of M-curves, totally positive Grassmannians and KP2-solitons" - Commun. Math. Phys. 2018, v. 361, Issue 3, pp. 1029-1081; doi:/10.1007/s00220-018-3123-y; - Available at the arxiv.org/archive/nlin arXiv:1506.00563 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  29. Grinevich P.G., Santini P.M. "The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes" - Physics Letters A, 2018, v. 382, pp. 973-979; doi:10.1016/j.physleta.2018.02.014; - Available at the arxiv.org/archive/nlin.SI arXiv:1708.04535 e-Print archive: Abstract | Tex file | Pdf file
  30. Grinevich P.G., Novikov S.P. "Singular solitons and spectral meromorphy" - Uspekhi Mathematicheskich Nauk, 2017, v. 72, No. 6(432), pp. 113-138 (in Russian); doi:10.4213/rm9806; English translation - Russian Mathematical Surveys, 2017, v.72, No. 6, pp. 1083-1107; doi:10.1070/RM9806.
  31. Grinevich P.G., Novikov R.G. "Multipoint scatterers with bound states at zero energy" - Theoretical and Mathematical Physics, 2017, v.193, №2; pp. 309-314; doi:10.4213/tmf9349; English translation - "Multipoint scatterers with bound states at zero energy" - Theoret. and Math. Phys., 2017, v.193, No.2, pp. 1675-1679; doi:10.1134/S0040577917110071; - Available at the hal archive: hal-01378022; and arxiv.org/archive/math.SP arXiv:1610.02319 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  32. Adler, V.E., Berest Yu. Yu., Buchstaber V.M., Grinevich P.G., Dubrovin B.A., Krichever I.M., Novikov S.P., Sergeev A.N., Feigin M.V., Felder G., Ferapontov E.V., Chalykh O.A., Etingof P.I. "Alexander Petrovich Veselov (on his 60th birthday)" - Uspekhi Mathematicheskich Nauk, 2016, v. 71, No. 6(432), pp. 172-188 (in Russian); doi:10.4213/rm9734; English translation - Russian Mathematical Surveys, 2016, v.71, No. 6, pp. 1159-1176; doi:10.1070/RM9734
  33. Grinevich P.G., Novikov S.P. "On s-meromorphic ordinary differential operators" - Uspekhi Mathematicheskich Nauk, 2016, v. 71, No. 6(432), pp. 161-162 (in Russian); doi:10.4213/rm9746; English translation - Russian Mathematical Surveys, 2016, v.71, No. 6, pp. 1143-1145; doi:10.1070/RM9746.
  34. Grinevich P.G., Novikov R.G. "Moutard transform approach to generalized analytic functions with contour poles" - Bulletin des sciences mathématiques, 2016, v. 140, issue 6, pp. 638-656; doi:10.1016/j.bulsci.2016.01.003; - Available at the hal archive: hal-01249043; and arxiv.org/archive/math.CV arXiv:1512.08874 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  35. Grinevich P.G., Novikov R.G. "Generalized analytic functions, Moutard-type transforms, and holomorphic maps" - Funct. Anal. i ego Pril., 2016, v.50, №2, pp. 81-84 (in Russian); doi:10.4213/faa3237; English translation: Funct. Anal. Appl. 2016, v. 50, Issue 2, pp.150-152; doi:10.1007/s10688-016-0140-5; - Available at the hal archive: hal-01234004v1; and arxiv.org/archive/math.CV arXiv:1512.00343 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  36. Grinevich P.G., Santini P.M. "An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects" -Theoretical and Mathematical Physics, 2016, v. 189, №1, pp. 59-68; doi:10.4213/tmf9098 ; English translation: Theoretical and Mathematical Physics, 2016, v. 189:1, pp. 1450-1458; doi:10.1134/S0040577916100056; - Available at the arxiv.org/archive/nlin.SI arXiv:1511.04436 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  37. Grinevich P.G., Novikov R.G. "Moutard transform for the generalized analytic functions" - The Journal of Geometric Analysis, 2016, v. 26, Issue 4, pp 2984-2995; doi:10.1007/s12220-015-9657-8; - Available at the hal archive: hal-01222481v1; and arxiv.org/archive/math.AP arXiv:1510.08764 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  38. Grinevich P.G., Novikov S.P. "On the s-meromorphic OD operators" - Available at the arxiv.org/archive/math-ph arXiv:1510.06770 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  39. Grinevich P.G., Santini P.M. "Nonlocality and the inverse scattering transform for the Pavlov equation" - Studies in Applied Mathematics, 2016, v. 137, Issue 1, pp. 10-27; doi:10.1111/sapm.12127; - Available at the arxiv.org/archive/nlin arXiv:1507.08205 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  40. Grinevich P.G., Santini P.M., Wu D. "The Cauchy problem for the Pavlov equation" - Nonlinearity, 2015, v. 28, No. 11, pp. 3709-3754; doi:10.1088/0951-7715/28/11/3709; - Available at the arxiv.org/archive/math-ph arXiv:1310.5834 e-Print archive: Abstract Tex file | Ps file | Pdf file
  41. Grinevich P.G., Mironov A.E., Novikov S.P. "On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator" - Uspekhi Mathematicheskich Nauk, 2015, v. 70, No. 2(422), pp. 109-140 (in Russian); doi:10.4213/rm9650; English translation: - Russian Mathematical Surveys, 2015, v. 70:2, pp. 299-329; doi:10.1070/RM2015v070n02ABEH004948
  42. Grinevich P.G. "Elements of the Riemann surfaces theory and the Riemann-Roch theorem" - In: Geometrical methods in mathematical physics 2. Lectures at summer school. Voskresenskoe 25-29.06.2012- Moscow, MAKS Press 2014, pp. 29-60.
  43. Grinevich P.G., Novikov S.P. "Spectrally Meromorphic Operators and Nonlinear Systems" - Uspekhi Mathematicheskich Nauk, 2014, v. 69, No. 5(419), pp. 163-164 (in Russian); doi:10.4213/rm9621; English translation - Russian Mathematical Surveys, 2014, v. 69, No. 5, pp. 924-926; doi:10.1070/RM2014v069n05ABEH004922
  44. Grinevich P.G., Novikov S.P. "Spectral Meromorphic Operators and Nonlinear Systems" arxiv.org/archive/math arXiv:1409.6349 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  45. Grinevich P.G., Novikov R.G. "Faddeev eigenfunctions for multipoint potentials" - Eurasian Journal of Mathematical and Computer Applications, 2013, Volume 1, Issue 2, pp. 76-91; - Available at the hal archive: hal-00747888, version 1; and arxiv.org/archive/math-ph arXiv:1211.0292 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  46. Grinevich P.G., Novikov S.P. "Singular soliton operators and indefinite metrics" - Bulletin of the Brazilian Mathematical Society, New Series, 2013, v. 44, No. 4, pp. 809-840; doi:10.1007/s00574-013-0035-5;
  47. Grinevich P.G., Novikov S.P. "Discrete SLn - connections and self-adjoint difference operators on two-dimensional manifolds" - Uspekhi Mathematicheskich Nauk, 2013, v. 68, No. 5(413) , pp. 81-110; doi:10.4213/rm9553; English translation - Russian Mathematical Surveys, 2013, v. 68, No. 5 , pp. 861-887; doi:10.1070/RM2013v068n05ABEH004859; - The preliminarily version is available at the arxiv.org/archive/math-ph arXiv:1207.1729 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  48. Grinevich P.G., Santini P.M. "Holomorphic eigenfunctions of the vector field associated with the dispersionless Kadomtsev-Petviashvili equation" - Journal of Differential Equations, 2013, v. 255, No. 7, pp. 1469-1491; doi:10.1016/j.jde.2013.05.010; - Available at the arxiv.org/archive/math-ph arXiv:1111.4446 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  49. Grinevich P.G., Novikov R.G. "Faddeev eigenfunctions for point potentials in two dimensions" - Physics Letters A, 2012, v. 376, pp. 1102-1106; doi:10.1016/j.physleta.2012.02.025; - Available at the hal archive: hal-00632264, version 1; and arxiv.org/archive/math-ph arXiv:1110.3157 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  50. Grinevich P.G., Mironov A.E., Novikov S.P. "Two-dimensional Pauli operator in a magnetic field" - Fizika nizkikh temperatur, 2011, v. 37, №9-10, p. 1040-1045; English translation - Low temperature physics, 2011, v. 37, pp. 829-833; doi:10.1063/1.3670025.
  51. Grinevich P.G., Novikov S.P. "Singular solitons and indefinite metrics" - Available at the arxiv.org/archive/math arXiv:1103.2505 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  52. Grinevich P.G., Mironov A.E., Novikov S.P. "Erratum" - Teoreticheskaia i matematicheskaia fizika, 2011, v. 166, №2, p. 320 (in Russian); doi:10.4213/tmf6613; English translation - Theoretical and Mathematical Physics, 2011, v. 166, №2, p. 278; doi:10.1007/s11232-011-0022-1.
  53. Grinevich P.G., Novikov S.P. "Singular solitons and indefinite metrics" - Dokl. Akad. Nauk, 2011, V. 436, №3, pp. 302-305 (in Russian); English translation - Doklady Mathematics, 2011, v. 83, №1, pp. 56-58; doi:10.1134/S1064562411010170e.
  54. Grinevich P.G., Mironov A.E., Novikov S.P. "On the Nonrelativistic 2D Purely Magnetic Supersymmetric Pauli Operator" - Available at the arxiv.org/archive/math arXiv:1101.5678 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  55. Grinevich P.G., Mironov A.E., Novikov S.P. "2D-Schrodinger Operator, (2+1) evolution systems and new reductions, 2D-Burgers hierarchy and inverse problem data" - Uspekhi. Mat. Nauk, 2010, v. 65, No 3(393), pp. 195-196 (in Russian); doi:10.4213/rm9363; English translation - Russian Mathematical Surveys, 2010, v. 65, No 3, pp. 580-582; doi:10.1070/RM2010v065n03ABEH004685; - Available at the arxiv.org/archive/math arXiv:1005.0612 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  56. Grinevich P.G., Mironov A.E., Novikov S.P. "On the zero level of purely magnetic nonrelativistic 2D Pauli Operators (spin=1/2)" - Teoreticheskaia i matematicheskaia fizika, 2010, v. 164, No 3, pp. 333-353 (in Russian); doi:10.4213/tmf6543; English translation - Theoretical and Mathematical Physics, 2010, v. 164, No 3, pp. 1110-1127; doi:10.1007/s11232-010-0089-0; - Available at the arxiv.org/archive/math arXiv:1004.1157 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  57. Grinevich P.G., Mironov A.E., Novikov S.P. "New Reductions and Nonlinear Systems for 2D Schrodinger Operators" - Available at the arxiv.org/archive/math arXiv:1001.4300 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  58. Abenda S., Grinevich P. "Periodic billiard orbits on n-dimensional ellipsoids with impacts on confocal quadrics and isoperiodic deformations" - Journal of Geometry and Physics, October 2010, v. 60, Issue 10, pp. 1617-1633; doi:10.1016/j.geomphys.2010.06.001; - Available at the arxiv.org/archive/nlin arXiv:0903.1980 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  59. Grinevich P.G., Novikov S.P. "Singular Finite-Gap Operators and Indefinite Metric. I" - Uspekhi. Mat. Nauk, 2009, v. 64, No 4, pp. 45-72 (in Russian); doi:10.4213/rm9307; - English translation - Russian Mathematical Surveys, 2009, v. 64, No 4, pp. 625-650; doi:10.1070/RM2009v064n04ABEH004629; Isaac Newton Institute for Mathematical Sciences preprint NI09030-DIS - Available at the arxiv.org/archive/math arXiv:0903.3976 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  60. 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; doi:10.1134/S0081543809030031; - Available at the arxiv.org/archive/math arXiV:0812.2494 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  61. 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 - Available at the arxiv.org/archive/math arXiv:0801.4143 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  62. 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. - Available at the arxiv.org/archive/nlin arXiv:nlin/0609063 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  63. 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); doi:10.4213/rm7483; - English translation: Russian Mathematical Surveys, 2007, v. 62, No 4, pp. 799-801; doi:10.1070/RM2007v062n04ABEH004438.
  64. 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; doi:10.1093/imrn/rnm005; - Available at the arxiv.org/archive/math arXiv:math/0611215 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  65. 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; doi:10.1016/j.physd.2007.05.002; - Available at the arxiv.org/archive/nlin arXiv:nlin/0607031 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  66. 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; doi:10.1063/1.2406056; - Available at the arxiv.org/archive/nlin arXiv:nlin/0410046 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  67. Grinevich P.G. "∂-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.
  68. 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; doi:10.1090/trans2/212/08; - Available at the arxiv.org/archive/nlin arXiv:nlin/0307026 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  69. 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; doi:10.1063/1.1588742; - Available at the arxiv.org/archive/math-ph arXiv:math-ph/0303039 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  70. 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; doi:10.1002/cpa.10081; - Available at the arxiv.org/archive/math-ph arXiv:math-ph/0111039 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  71. 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); doi:10.4213/rm443; - English translation: Russ. Math. Surveys, 2001, v. 56, №5, pp. 980-981; doi:10.1070/RM2001v056n05ABEH000443.
  72. 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; doi:10.1016/S0167-2789(01)00155-5; - Available at the arxiv.org/archive/nlin arXiv:nlin/0002020 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  73. 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.
  74. 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); doi:10.4213/rm333; - English translation: Russian Math. Surveys, 2000, v. 55, №6, pp. 1015-1083; doi:10.1070/RM2000v055n06ABEH000333.
  75. Grinevich P.G, Novikov R.G. "Discrete spectrum for n-cell potentials." - Rapport de Recherche №98/10-2, Universite de Nantes; - Available at the arxiv.org/archive/math-ph arXiv:math-ph/9811014 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  76. Grinevich P.G. "Complex manifold", "Conformal transformation", "Holomorphic form", "Holomorphic map". - Mathematical physics. Encyclopedia. (in Russian). Editor-in-chief - L.D.Faddeev. 1998.
  77. 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; doi:10.1016/S0393-0440(97)00038-7; - Available at the arxiv.org/archive/math.DG arXiv:dg-ga/9702015 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  78. 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; - Available at the arxiv.org/archive/math.DG arXiv:dg-ga/9703020 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  79. 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; doi:10.1023/A:1007333509613; - Available at the arxiv.org/archive/nlin arXiv:solv-int/9509010 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  80. 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.
  81. 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; doi:10.1007/BF02099609; - Available at the arxiv.org/archive/nlin arXiv:solv-int/9410003 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  82. 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; - Available at the arxiv.org/archive/nlin arXiv:solv-int/9501006 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  83. 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; doi:10.1016/0167-2789(95)00139-U; SFB 288 preprint №150, Berlin, Dec 1994; - Available at the arxiv.org/archive/nlin arXiv:solv-int/9412005 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  84. 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. - Available at the arxiv.org/archive/nlin arXiv:solv-int/9509004 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  85. P.G.Grinevich. "Fast decaying potentials on the finite-gap background and the ∂-bar-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; doi:10.1007/BF01016145.
  86. 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. - Available at the arxiv.org/archive/nlin arXiv:solv-int/9501002 e-Print archive: Abstract | Tex file | Ps file | Pdf file
  87. 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; doi:10.1007/978-3-642-77769-1_19.
  88. 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; doi:10.1007/978-3-642-58045-1_14.
  89. Benderskii V.A., Grinevich P.G., Makarov D.E. "Quantum chemical dynamics in two dimensions." - Chem. Phys., 1993, v. 170, pp. 275-293; doi:10.1016/0301-0104(93)85114-N.
  90. 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; doi:10.1016/0301-0104(92)80176-V.
  91. 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).
  92. 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; doi:10.1007/978-3-642-84039-5_32.
  93. 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.
  94. 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.
  95. 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; doi:10.1007/BF01077923.
  96. Grinevich P.G., Orlov A.Yu. "Virasoro action on Riemann surfaces, Grassmanians, det ∂-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; doi:10.1007/978-3-642-84000-5_7; - The first version of this text is avaliable at the arxiv.org/archive/math-ph math-ph/9804019 e-Print archive: Abstract| Tex file | Ps file | Pdf file
  97. Grinevich P.G., Orlov A.Yu. Wilson tau - function and det ∂-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.
  98. 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.
  99. Grinevich P.G. "Rapidly decreasing potentials on a background of finite-zone potentials and the ∂-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; doi:10.1007/BF01078948.
  100. 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.
  101. 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.
  102. 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; doi:10.1007/BF00682148.
  103. 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; doi:10.1007/BF01077719.
  104. 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; doi:10.1007/BF01037878.
  105. 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; doi:10.1070/IM1987v028n03ABEH000892.
  106. Grinevich P.G. Manakov S.V. "Inverse scattering problem for the two-dimensional Schrodinger operator, ∂-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; doi:10.1007/BF01077263.
  107. 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.
  108. 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; doi:10.1007/BF01077292.
  109. 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.
  110. 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; doi:10.1007/BF01081804.
  111. 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; doi:10.1007/BF01081803.

Back to the Home Page