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TMF, 1999, Volume 118, Number 3, Pages 413–422 (Mi tmf714)  

This article is cited in 3 scientific papers (total in 3 papers)

Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation

V. R. Kudashev, B. I. Suleimanov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: Analogues of the Pearcey integral describe the small dispersion influence on the beginning of spontaneous-vanishing processes for the nonlinear geometric optic approximation amplitude, which is a solution of equations of the focusing nonlinear Schrödinger equation type. The asymptotic behavior as $x^2+t^2\to\infty$ of these analogues is considered. For $x^2+t^2\to\infty$, the special functions under consideration have a domain of small-amplitude high-frequency oscillations, which occur on the background of the nonzero-amplitude nonlinear geometric optic approximation.

DOI: https://doi.org/10.4213/tmf714

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English version:
Theoretical and Mathematical Physics, 1999, 118:3, 325–332

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Citation: V. R. Kudashev, B. I. Suleimanov, “Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation”, TMF, 118:3 (1999), 413–422; Theoret. and Math. Phys., 118:3 (1999), 325–332

Citation in format AMSBIB
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\by V.~R.~Kudashev, B.~I.~Suleimanov
\paper Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation
\jour TMF
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\pages 413--422
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\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
\issue 3
\pages 325--332
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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. 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
    2. Ershov A.A., Suleimanov B.I., “Some Features of Bending of a Rod Under a Strong Longitudinal Compression”, Russ. J. Math. Phys., 24:2 (2017), 216–233  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    3. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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