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Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit

TitleSolitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit
Publication TypeJournal Article
Year of Publication2010
AuthorsGrava, T, Claeys, T
JournalSIAM J. Math. Anal. 42 (2010) 2132-2154
Abstract

We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation.

URLhttp://hdl.handle.net/1963/3839
DOI10.1137/090779103

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