Author:
He Feng-Jing,Fan En-Gui,Xu Jian
Abstract
Abstract
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) −6q(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 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.
Subject
Physics and Astronomy (miscellaneous)
Cited by
28 articles.
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