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Title: Painleve II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small dispersion limit
Authors: Claeys, Tom ×
Grava, Tamara #
Issue Date: Feb-2010
Publisher: John Wiley & Sons
Series Title: Communications on Pure and Applied Mathematics vol:63 issue:2 pages:203-232
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.
ISSN: 0010-3640
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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