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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 245–253 (Mi timm826)  

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

Asymptotics of the Gurevich–Pitaevskii universal special solution of the Korteweg–de Vries equation as $|x|\to\infty$

B. I. Suleimanov

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

Abstract: A complete asymptotic expansion as $x\to\pm\infty$ of the Gurevich–Pitaevskii universal special solution of the Korteweg–de Vries equation $u_t+u_{xxx}+uu_x=0$ is constructed and validated. The expansion is infinitely differentiable in the variables $t$ and $x$ and, together with the asymptotic expansions of all its derivatives in independent variables, is uniform on any compact interval of variation of the time $t$.

Keywords: Korteweg–de Vries equation, nonlinear Schrödinger equation, isomonodromy, asymptotic expansion.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 281, suppl. 1, 137–145

Bibliographic databases:

UDC: 517.9
Received: 27.09.2011

Citation: B. I. Suleimanov, “Asymptotics of the Gurevich–Pitaevskii universal special solution of the Korteweg–de Vries equation as $|x|\to\infty$”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 245–253; Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 137–145

Citation in format AMSBIB
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\by B.~I.~Suleimanov
\paper Asymptotics of the Gurevich--Pitaevskii universal special solution of the Korteweg--de Vries equation as~$|x|\to\infty$
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 2
\pages 245--253
\mathnet{http://mi.mathnet.ru/timm826}
\elib{https://elibrary.ru/item.asp?id=17736204}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 281
\issue , suppl. 1
\pages 137--145
\crossref{https://doi.org/10.1134/S0081543813050131}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84879178142}


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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, ““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
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