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Zap. Nauchn. Sem. LOMI, 1991, Volume 187, Pages 110–128 (Mi znsl4865)  

This article is cited in 6 scientific papers (total in 6 papers)

The second Painlevé equation at a problem about nonlinear effects near caustics

B. I. Suleimanov


Abstract: An asymptotics at large time for nonlinear Schrödinger equation is studied in a critical case produced by some problems concerning nonlinear effects near caustics. The asymptotics is described in terms of the second Painlevé transcendent.

Full text: PDF file (686 kB)

English version:
Journal of Mathematical Sciences, 1995, 73:4, 482–493

Bibliographic databases:

UDC: 517.9

Citation: B. I. Suleimanov, “The second Painlevé equation at a problem about nonlinear effects near caustics”, Differential geometry, Lie groups and mechanics. Part 12, Zap. Nauchn. Sem. LOMI, 187, Nauka, St. Petersburg, 1991, 110–128; J. Math. Sci., 73:4 (1995), 482–493

Citation in format AMSBIB
\Bibitem{Sul91}
\by B.~I.~Suleimanov
\paper The second Painlev\'e equation at a problem about nonlinear effects near caustics
\inbook Differential geometry, Lie groups and mechanics. Part~12
\serial Zap. Nauchn. Sem. LOMI
\yr 1991
\vol 187
\pages 110--128
\publ Nauka
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4865}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1111907}
\zmath{https://zbmath.org/?q=an:0834.34008|0746.34013}
\transl
\jour J. Math. Sci.
\yr 1995
\vol 73
\issue 4
\pages 482--493
\crossref{https://doi.org/10.1007/BF02364570}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. R. Kudashev, B. I. Suleimanov, “Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation”, Theoret. and Math. Phys., 118:3 (1999), 325–332  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. B. I. Suleimanov, “Asymptotics of the Gurevich–Pitaevskii universal special solution of the Korteweg–de Vries equation as $|x|\to\infty$”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 137–145  mathnet  crossref  isi  elib
    3. B. I. Suleimanov, ““Quantizations” of Higher Hamiltonian Analogues of the Painlevé I and Painlevé II Equations with Two Degrees of Freedom”, Funct. Anal. Appl., 48:3 (2014), 198–207  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. B. I. Suleimanov, “Effect of a small dispersion on self-focusing in a spatially one-dimensional case”, JETP Letters, 106:6 (2017), 400–405  mathnet  crossref  crossref  isi  elib
    5. B. I. Suleimanov, “Ob analogakh funktsii volnovykh katastrof, yavlyayuschikhsya resheniyami nelineinykh integriruemykh uravnenii”, Differentsialnye uravneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 163, VINITI RAN, M., 2019, 81–95  mathnet  mathscinet
    6. B. I. Suleimanov, A. M. Shavlukov, “Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation”, Ufa Math. J., 13:2 (2021), 99–106  mathnet  crossref  isi
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