Long-Time Asymptotics for the Nonlocal MKdV Equation

被引：0
|
作者：
何丰敬 [1 ]
范恩贵 [1 ]
徐建 [2 ]
机构：
[1] School of Mathematical Sciences, Fudan University
[2] College of Science, University of Shanghai for Science and Technology
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;
D O I：
暂无
中图分类号：
O175.29 [非线性偏微分方程];
学科分类号：
070104 ;
摘要：
In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation(nonlocal mKdV) qt(x, t)+qxxx(x, t)-6 q(x, t)q(-x,-t)qx(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 m KdV 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
收藏
页码：475 / 488
页数：14
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