Prefer a chat interface with context about you and your work?
Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg—de Vries equation in the small‐dispersion limit
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 …