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Mat. Zametki, 1992, Volume 52, Issue 1, Pages 42–50 (Mi mz4653)  

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

Existence of a family of soliton-like solutions for the Kawahara equation

A. T. Il'ichev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Existence is proved for a family of soliton-like solutions for the nonlinear evolution equation $\mathbf{u}_t+\mathbf{uu}_x+\mathbf{u}_{xxx}-\mathbf{u}_{xxxxx}=0$. The problem is reduced to investigating the fixed points of the operator
$$ (Au)(x)=\int_{-\infty}^{\infty}k(x-y)u^2(y) dy, \quad \int_{-\infty}^{\infty}k(x)=1, $$
whose action is considered in a cone of Frechet functions that are continuous on the real axis.

Full text: PDF file (972 kB)

English version:
Mathematical Notes, 1992, 52:1, 662–668

Bibliographic databases:

UDC: 517
Received: 12.10.1990

Citation: A. T. Il'ichev, “Existence of a family of soliton-like solutions for the Kawahara equation”, Mat. Zametki, 52:1 (1992), 42–50; Math. Notes, 52:1 (1992), 662–668

Citation in format AMSBIB
\Bibitem{Ili92}
\by A.~T.~Il'ichev
\paper Existence of a family of soliton-like solutions for the Kawahara equation
\jour Mat. Zametki
\yr 1992
\vol 52
\issue 1
\pages 42--50
\mathnet{http://mi.mathnet.ru/mz4653}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1187712}
\zmath{https://zbmath.org/?q=an:0787.35082|0770.35060}
\transl
\jour Math. Notes
\yr 1992
\vol 52
\issue 1
\pages 662--668
\crossref{https://doi.org/10.1007/BF01247646}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992LC62500007}


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    This publication is cited in the following articles:
    1. A. T. Il'ichev, “Solitary waves in a cold plasma”, Math. Notes, 59:5 (1996), 518–524  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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