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.
作者
Feng-Jing He
En-Gui Fan
Jian Xu
何丰敬;范恩贵;徐建(School of Mathematical Sciences, Fudan University;College of Science, University of Shanghai for Science and Technology)
基金
Supported by National Science Foundation of China under Grant Nos.11671095,51879045
National Science Foundation of China under Grant No.11501365
Shanghai Sailing Program supported by Science and Technology Commission of Shanghai Municipality under Grant No.15YF1408100
Shanghai Youth Teacher Assistance Program No.ZZslg15056
