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

被引：4

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

收藏

页码：1607 / 1656

页数：50

相关论文

共 21 条

[1]

ABLOWITZ MJ, 1976, STUD APPL MATH, V55, P213

[2] Continuous approximation of breathers in one- and two-dimensional DNLS lattices [J].

Bambusi, D. ;

Penati, T. .

NONLINEARITY, 2010, 23 (01) :143-157

[3] Existence and stability of ground states for fully discrete approximations of the nonlinear Schrodinger equation [J].

Bambusi, Dario ;

Faou, Erwan ;

Grebert, Benoit .

NUMERISCHE MATHEMATIK, 2013, 123 (03) :461-492

[4] Optimality and resonances in a class of compact finite difference schemes of high order [J].

Bernier, Joackim .

CALCOLO, 2019, 56 (02)

[5] BOUNDS ON THE GROWTH OF HIGH DISCRETE SOBOLEV NORMS FOR THE CUBIC DISCRETE NONLINEAR SCHRODINGER EQUATIONS ON hZ [J].

Bernier, Joackim .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (06) :3179-3195

[6] On growth of Sobolev norms in linear Schrodinger equations with smooth time dependent potential [J].

Bourgain, J .

JOURNAL D ANALYSE MATHEMATIQUE, 1999, 77 (1) :315-348

[7] ORBITAL STABILITY OF STANDING WAVES FOR SOME NON-LINEAR SCHRODING EQUATIONS [J].

CAZENAVE, T ;

LIONS, PL .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 85 (04) :549-561

[8] Orbital Stability: Analysis Meets Geometry [J].

De Bievre, Stephan ;

Genoud, Francois ;

Nodari, Simona Rota .

NONLINEAR OPTICAL AND ATOMIC SYSTEMS: AT THE INTERFACE OF PHYSICS AND MATHEMATICS, 2015, 2146 :147-273

[9] THE DISCRETE SELF-TRAPPING EQUATION [J].

EILBECK, JC ;

LOMDAHL, PS ;

SCOTT, AC .

PHYSICA D-NONLINEAR PHENOMENA, 1985, 16 (03) :318-338

[10] Solitary wave dynamics in an external potential [J].

Fröhlich, J ;

Gustafson, S ;

Jonsson, BLG ;

Sigal, IM .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 250 (03) :613-642