Solitonic Asymptotics for the Korteweg–de Vries Equation in the Small Dispersion Limit

Tom Claeys, Tamara Grava

Research output: Contribution to journalArticle (Academic Journal)peer-review

23 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)2132-2154
Number of pages23
JournalSIAM Journal on Mathematical Analysis
Volume42
Issue number5
DOIs
Publication statusPublished - Sep 2010

Fingerprint Dive into the research topics of 'Solitonic Asymptotics for the Korteweg–de Vries Equation in the Small Dispersion Limit'. Together they form a unique fingerprint.

Cite this