Long-time asymptotic behavior for the complex short pulse equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Xu, Jian¹  Fan, Engui^2,3 

[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

[2] Fudan Univ, Sch Math Sci, Inst Math, Shanghai 200433, Peoples R China

[3] Fudan Univ, Key Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China

关键词: Complex short pulse equation;    Initial value problem;    Riemann-Hilbert problem;    Nonlinear steepest descent method;    Long-time asymptotics;   

DOI  :  10.1016/j.jde.2020.07.009

来源: Elsevier

【 摘 要 】

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 x 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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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