TY - JOUR
T1 - PainlevĂ© II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit
JF - Comm. Pure Appl. Math. 63 (2010) 203-232
Y1 - 2010
A1 - Tom Claeys
A1 - Tamara Grava
AB - 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.
PB - Wiley
UR - http://hdl.handle.net/1963/3799
U1 - 527
U2 - Mathematics
U3 - Mathematical Physics
ER -