@article {2010,
	title = {Painlev{\'e} II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit},
	journal = {Comm. Pure Appl. Math. 63 (2010) 203-232},
	number = {arXiv.org;0812.4142v1},
	year = {2010},
	publisher = {Wiley},
	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.},
	doi = {10.1002/cpa.20277},
	url = {http://hdl.handle.net/1963/3799},
	author = {Tom Claeys and Tamara Grava}
}
