The nonlinear Schroedinger equation: Solitons dynamics

被引：9

作者：

Benci, Vieri ^{[2
]}

Ghimenti, Marco ^{[1
]}

Micheletti, Anna Maria ^{[2
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy

[2] Univ Pisa, Dipartimento Matemat Applicata, I-56127 Pisa, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 249卷 / 12期

关键词：

Soliton dynamics; Nonlinear Schroedinger equation; Orbital stability; Concentration phenomena; Semiclassical limit; LINEAR SCHRODINGER EQUATIONS; SOLITARY WAVES; SEMICLASSICAL LIMIT; STABILITY THEORY; GROUND-STATES; EXISTENCE; DIMENSIONS; EVOLUTION; SYMMETRY;

D O I：

10.1016/j.jde.2010.09.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h -> 0. We prove that under suitable assumptions, the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenter q(h)(t) satisfies the equation q(h)(t) + del V (q(h) (t)) = H-h(t) where sup(t is an element of R)vertical bar H-h(t)vertical bar -> 0 as h -> 0. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：3312 / 3341

页数：30

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