Long-time asymptotic behavior for the complex short pulse equation

2017/12/21 by Xu, Jian, Fan, Engui
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1712.07815

Abstract

In this paper, we consider the initial value problem for the complex short pulse equation with a Wadati-Konno-Ichikawa type Lax pair. We show that the solution to the initial value problem has a parametric expression in terms of the solution of 2× 2-matrix Riemann-Hilbert problem, from which an implicit one-soliton solution is obtained on the discrete spectrum. While on the continuous spectrum we further establish the explicit long-time asymptotic behavior of the non-soliton solution by using Deift-Zhou nonlinear steepest descent method.

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