EXISTENCE AND STABILITY OF TRAVELING WAVES FOR DISCRETE NONLINEAR SCHRODINGER EQUATIONS OVER LONG TIMES

被引：3

作者：

Bernier, Joackim ^{[1
]}

Faou, Erwan ^{[1
]}

机构：

[1] Univ Rennes, INRIA, CNRS, IRMAR,UMR 6625, F-35000 Rennes, France

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2019年 / 51卷 / 03期

关键词：

discrete nonlinear Schrodinger equation; solitary waves; finite differences; continuous limit; GROUND-STATES; SOBOLEV-NORMS; ORBITAL STABILITY; SOLITARY WAVES; GROWTH; BOUNDS;

D O I：

10.1137/18M1186484

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem of existence and stability of solitary traveling waves for the one-dimensional discrete nonlinear Schrodinger equation with cubic nonlinearity, near the continuum limit. We construct a family of solutions close to the continuous traveling waves and prove their stability over long times. Applying a modulation method, we describe the dynamics near these discrete traveling waves over long times.

引用

页码：1607 / 1656

页数：50

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