Rarefaction Waves of the Korteweg-de Vries Equation via Nonlinear Steepest Descent
arXiv:1602.02427 · doi:10.1016/j.jde.2016.08.009
Abstract
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation with steplike initial data leading to a rarefaction wave. In addition to the leading asymptotic we also compute the next term in the asymptotic expansion of the rarefaction wave, which was not known before.
34 pages