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TMF, 1993, Volume 97, Number 2, Pages 213–226 (Mi tmf1734)  

This article is cited in 1 scientific paper (total in 1 paper)

Symmetries of Kadomtsev–Petviashvili equation, isomonodromic deformations, and nonlinear generalizations of the special functions of wave catastrophes

B. I. Suleimanova, I. T. Habibullinab

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
b Bashkir State University

Abstract: A special solution of the Kadomtsev–Petviashvili equation
$$u_{tx} + u_{xxxx} + 3u_{yy} + 3(u^2)_{xx} = 0,$$
that is a “nonlinear” analog of the special function of wave catastrophe corresponding to a singularity of swallowtail type is considered. On the basis of a symmetry analysis it is shown that the solution must simultaneously satisfy nonlinear ordinary differential equations with respect to all three independent variables. After “dressing” of the corresponding $\Psi$ function, equations with respect to a spectral parameter arise in a regular manner, and this indicates the possibility of applying the method of isomonodromic deformation.

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English version:
Theoretical and Mathematical Physics, 1993, 97:2, 1250–1258

Bibliographic databases:

Received: 05.10.1992

Citation: B. I. Suleimanov, I. T. Habibullin, “Symmetries of Kadomtsev–Petviashvili equation, isomonodromic deformations, and nonlinear generalizations of the special functions of wave catastrophes”, TMF, 97:2 (1993), 213–226; Theoret. and Math. Phys., 97:2 (1993), 1250–1258

Citation in format AMSBIB
\Bibitem{SulHab93}
\by B.~I.~Suleimanov, I.~T.~Habibullin
\paper Symmetries of Kadomtsev--Petviashvili equation, isomonodromic deformations, and nonlinear generalizations of the special functions of wave catastrophes
\jour TMF
\yr 1993
\vol 97
\issue 2
\pages 213--226
\mathnet{http://mi.mathnet.ru/tmf1734}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1257867}
\zmath{https://zbmath.org/?q=an:0801.35127}
\transl
\jour Theoret. and Math. Phys.
\yr 1993
\vol 97
\issue 2
\pages 1250--1258
\crossref{https://doi.org/10.1007/BF01016870}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993NK68000004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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