Painlevé II asymptotics near the leading edge of the oscillatory zone 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

In the small-dispersion limit, solutions to the Korteweg—de Vries equation develop an interval of fast oscillations after a certain time. We obtain a universal asymptotic expansion for the Korteweg—de Vries solution near the leading edge of the oscillatory zone up to second-order corrections. This expansion involves the Hastings-McLeod solution of the Painlevé II equation. We prove our results using the Riemann-Hilbert approach
Original languageEnglish
Pages (from-to)203-232
Number of pages31
JournalCommunications on Pure and Applied Mathematics
Volume63
Issue number2
Early online date3 Mar 2009
DOIs
Publication statusPublished - Feb 2010

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