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

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

References in corpus (3)

• Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent
• On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations
• Inverse scattering theory for Schrödinger operators with steplike potentials

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• Riemann-Hilbert Theory without local Parametrix Problems: Applications to Orthogonal Polynomials
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• The effect of a positive bound state on the KdV solution. A case study