High-speed excited multi-solitons in nonlinear Schrodinger equations

被引：34

作者：

Cote, Raphael ^{[1
]}

Le Coz, Stefan ^{[2
]}

机构：

[1] Ecole Polytech, CMLS, F-91128 Palaiseau, France

[2] Univ Paris 06, Lab Jacques Louis Lions, F-75252 Paris 05, France

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2011年 / 96卷 / 02期

关键词：

Multi-solitons; Nonlinear Schrodinger equations; Excited states; SCALAR FIELD-EQUATIONS; SUPERCRITICAL GKDV EQUATIONS; SOLITARY WAVES; MULTISOLITON SOLUTIONS; THRESHOLD SOLUTIONS; EXPONENTIAL DECAY; STABILITY THEORY; STANDING WAVES; GROUND-STATES; NLS;

D O I：

10.1016/j.matpur.2011.03.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the nonlinear Schrodinger equation in R-d i partial derivative(t)u + Delta u + f(u) = 0. For d >= 2. this equation admits traveling wave solutions of the form e(i omega t)Phi(x) (up to a Galilean transformation), where Phi is a fixed profile, solution to -Delta Phi + omega Phi = f(Phi), but not the ground state. This kind of profiles are called excited states. In this paper, we construct solutions to NLS behaving like a sum of N excited states which spread up quickly as time grows (which we call multi-solitons). We also show that if the flow around one of these excited states is linearly unstable, then the multi-soliton is not unique, and is unstable. (C) 2011 Elsevier Masson SAS. All rights reserved.

引用

页码：135 / 166

页数：32

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