Abstract
AbstractIn 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. © 2009 Wiley Periodicals, Inc.
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