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arXiv · 1602.02427

Rarefaction Waves of the Korteweg-de Vries Equation via Nonlinear Steepest Descent

Kyrylo Andreiev·Iryna Egorova·Till Luc Lange·Gerald Teschl
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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.

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Kyrylo Andreiev, Iryna Egorova, Till Luc Lange, Gerald Teschl. 2016-09-19. Rarefaction Waves of the Korteweg-de Vries Equation via Nonlinear Steepest Descent. https://doi.org/10.1016/j.jde.2016.08.009

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