Long-time asymptotics for a mixed nonlinear Schrodinger equation with the Schwartz initial data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:489

Article

Cheng, Qiaoyuan¹  Fan, Engui¹ 

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

关键词: Mixed nonlinear Schrodinger equation;    Lax pair;    Riemann-Hilbert problem;    Deift-Zhou steepest descent method;    Long-time asymptotics;   

DOI  :  10.1016/j.jmaa.2020.124188

来源: Elsevier

【 摘 要 】

In this paper, we define a general analytical domain and two reflection coefficients to study the long-time asymptotics for a defocusing mixed nonlinear Schrodinger equation with the Schwartz initial data. It is shown that the solution of the initial value problem for the mixed Schrodinger equation can be expressed in terms of the solution associated with a Riemann-Hilbert problem. The long-time asymptotic of the mixed Schrodingerequation is further obtained via the Deift-Zhou nonlinear steepest descent method. The long-time asymptotic for the classical Schrodinger equation, derivative Schrodinger equation and modified Schrodinger equation are obtained directly from our results as special cases. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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