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arXiv · 1712.07815

Long-time asymptotic behavior for the complex short pulse equation

Jian Xu·Engui Fan
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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 $2\times 2$-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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Jian Xu, Engui Fan. 2017-12-21. Long-time asymptotic behavior for the complex short pulse equation. https://arxiv.org/abs/1712.07815

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