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Zh. Mat. Fiz. Anal. Geom., 2017, Volume 13, Number 4, Pages 325–343 (Mi jmag677)  

On the long-time asymptotics for the Korteweg–de Vries equation with steplike initial data associated with rarefaction waves

K. Andreiev, I. Egorova

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine

Abstract: We discuss an asymptotical behavior of the rarefaction wave for the KdV equation in the region behind the wave front. The first and the second terms of the asymptotical expansion for such a solution with respect to large time were derived without detailed analysis in [1]. In the present work, we correct the formula for the second term by investigating the corresponding parametrix problem. We also study an influence of the resonance on the asymptotical behavior of the solution.

Key words and phrases: KdV equation, rarefaction wave, parametrix problem.

DOI: https://doi.org/10.15407/mag13.04.325

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Bibliographic databases:

MSC: 37K40, 35Q53, 35Q15
Received: 15.08.2017
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Citation: K. Andreiev, I. Egorova, “On the long-time asymptotics for the Korteweg–de Vries equation with steplike initial data associated with rarefaction waves”, Zh. Mat. Fiz. Anal. Geom., 13:4 (2017), 325–343

Citation in format AMSBIB
\Bibitem{AndEgo17}
\by K.~Andreiev, I.~Egorova
\paper On the long-time asymptotics for the Korteweg–de Vries equation with steplike initial data associated with rarefaction waves
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2017
\vol 13
\issue 4
\pages 325--343
\mathnet{http://mi.mathnet.ru/jmag677}
\crossref{https://doi.org/10.15407/mag13.04.325}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000417388000001}


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