Long-Time Asymptotics for the Nonlocal MKdV Equation

被引：32

作者：

He, Feng-Jing ^{[1
]}

Fan, En-Gui ^{[1
]}

Xu, Jian ^{[2
]}

机构：

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

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

来源：

COMMUNICATIONS IN THEORETICAL PHYSICS | 2019年 / 71卷 / 05期

基金：

美国国家科学基金会;

关键词：

nonlocal mKdV equation; Riemann-Hilbert problem; Deift-Zhou nonlinear steepest-descent; long-time asymptotics; NONLINEAR SCHRODINGER-EQUATION; INVERSE SCATTERING TRANSFORM; RIEMANN-HILBERT PROBLEMS; STEEPEST DESCENT METHOD; DE-VRIES EQUATION;

D O I：

10.1088/0253-6102/71/5/475

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation (nonlocal mKdV) q(t) (x, t)+q(xxx)(x, t)-6q(x, t)q (-x, -t)q(x)(x, t) = 0, which can be viewed as a generalization of the local classical mKdV equation. We first formulate the Riemann Hilbert problem associated with the Cauchy problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear steepest-descent method to analyze the long-time asymptotics for the solution of the nonlocal mKdV equation. In contrast with the classical mKdV equation, we find some new and different results on long-time asymptotics for the nonlocal mKdV equation and some additional assumptions about the scattering data are made in our main results.

引用

页码：475 / 488

页数：14

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