%0 Journal Article %J Comm. Pure Appl. Math. 63 (2010) 203-232 %D 2010 %T Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit %A Tom Claeys %A Tamara Grava %X 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. %B Comm. Pure Appl. Math. 63 (2010) 203-232 %I Wiley %G en_US %U http://hdl.handle.net/1963/3799 %1 527 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-26T16:48:15Z\\nNo. of bitstreams: 1\\n0812.4142v1.pdf: 343118 bytes, checksum: 4bf2fa3751076c18466f29e1163acc09 (MD5) %R 10.1002/cpa.20277