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TMF, 1994, Volume 98, Number 2, Pages 197–206 (Mi tmf1971)  

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

Influence of weak nonlinearity on the high-frequency asymptotics in caustic rearrangements

B. I. Suleimanov

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

Abstract: A study is made of the influence of weak nonlinearity on the structure of the high-frequency asymptotics in the neighborhood of singular points of caustics. The properties of the resulting nonlinear analogs of the special functions of wave catastrophes are described. It is shown that these nonlinear special functions satisfy ordinary differential equations.

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English version:
Theoretical and Mathematical Physics, 1994, 98:2, 132–138

Bibliographic databases:

Received: 10.02.1993

Citation: B. I. Suleimanov, “Influence of weak nonlinearity on the high-frequency asymptotics in caustic rearrangements”, TMF, 98:2 (1994), 197–206; Theoret. and Math. Phys., 98:2 (1994), 132–138

Citation in format AMSBIB
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\by B.~I.~Suleimanov
\paper Influence of weak nonlinearity on the high-frequency asymptotics in caustic rearrangements
\jour TMF
\yr 1994
\vol 98
\issue 2
\pages 197--206
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1291374}
\zmath{https://zbmath.org/?q=an:0817.35105}
\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 98
\issue 2
\pages 132--138
\crossref{https://doi.org/10.1007/BF01015791}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994PA59100003}


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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, “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
    2. 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
    3. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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