Painleve II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small dispersion limit

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dc.creatorClaeys, T.
dc.creatorGrava, T.
dc.date2008-12-22
dc.date.accessioned2026-07-07T12:21:12Z
dc.date.available2026-07-07T12:21:12Z
dc.descriptionIn 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.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/0812.4142
dc.identifierhttp://arxiv.org/abs/0812.4142
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213292
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subjectClassical Analysis and ODEs
dc.subject35Q53; 33E17; 35Q15
dc.titlePainleve II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small dispersion limit
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