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math-ph2008
Painleve II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small dispersion limit
T. Claeys, T. Grava
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…
math-ph2008★ 82 cited
Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach
Tom Claeys, Tamara Grava
We obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrop…