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Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent

arXiv:0807.5041 · doi:10.1007/s11040-009-9062-2

Abstract

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction to this method.

31 pages