| Title | Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit |
| Publication Type | Journal Article |
| Year of Publication | 2010 |
| Authors | Claeys, T, Grava, T |
| Journal | Comm. Pure Appl. Math. 63 (2010) 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 Painlev\\\\\\\'e II equation. We prove our results using the Riemann-Hilbert approach. |
| URL | http://hdl.handle.net/1963/3799 |
| DOI | 10.1002/cpa.20277 |
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