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Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions

TitleNumerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions
Publication TypeJournal Article
Year of Publication2012
AuthorsGrava, T, Klein, C
JournalPhysica D 241, nr. 23-24 (2012): 2246-2264
KeywordsKorteweg-de Vries equation
Abstract

We study numerically the small dispersion limit for the Korteweg-de Vries
(KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ for $\epsilon\ll1$ and give a
quantitative comparison of the numerical solution with various asymptotic
formulae for small $\epsilon$ in the whole $(x,t)$-plane. The matching of the
asymptotic solutions is studied numerically.

DOI10.1016/j.physd.2012.04.001

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