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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 2, Pages 80–86 (Mi ufa149)  

This article is cited in 2 scientific papers (total in 2 papers)

Phase shift for the common solution of the KdV and the fifth order differential equation

R. N. Garifullin

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

Abstract: We investigate the special solution of Korteweg–de Vries equation. This solution describes the influence of small dispersion to a process of transformation from weak to strong discontinuities in inviscid fluid dynamics. This solution also satisfies the fifth order ordinary differential equation. We construct the asymptotic solution in the Witham zone up to a phase shift. We obtain an the equation for phase shift and, using the numerical experiments, we choose the concrete solution of this equation. This solution is a constant function.

Keywords: phase shift, Korteweg–de Vries equation, nondissipative shock waves.

Full text: PDF file (209 kB)
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Bibliographic databases:
UDC: 517.928
Received: 19.05.2012

Citation: R. N. Garifullin, “Phase shift for the common solution of the KdV and the fifth order differential equation”, Ufimsk. Mat. Zh., 4:2 (2012), 80–86

Citation in format AMSBIB
\Bibitem{Gar12}
\by R.~N.~Garifullin
\paper Phase shift for the common solution of the KdV and the fifth order differential equation
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 2
\pages 80--86
\mathnet{http://mi.mathnet.ru/ufa149}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3432645}


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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. R. N. Garifullin, “On simultaneous solution of the KdV equation and a fifth-order differential equation”, Ufa Math. J., 8:4 (2016), 52–61  mathnet  crossref  isi  elib
    2. V. A. Pavlenko, B. I. Suleimanov, ““Quantizations” of isomonodromic Hamilton system $H^{\frac{7}{2}+1}$”, Ufa Math. J., 9:4 (2017), 97–107  mathnet  crossref  isi  elib
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