STABILITY OF SMALL SOLITARY WAVES FOR THE ONE-DIMENSIONAL NLS WITH AN ATTRACTIVE DELTA POTENTIAL

被引：11

作者：

Masaki, Satoshi ^{[1
]}

Murphy, Jason ^{[2
]}

Segata, Jun-ichi ^{[3
]}

机构：

[1] Osaka Univ, Grad Sch Engn Sci, Dept Syst Innovat, Osaka, Japan

[2] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA

[3] Tohoku Univ, Math Inst, Sendai, Miyagi, Japan

来源：

ANALYSIS & PDE | 2020年 / 13卷 / 04期

关键词：

NLS; solitary waves; asymptotic stability; delta potential; NONLINEAR SCHRODINGER-EQUATIONS; ASYMPTOTIC STABILITY; SCATTERING; DYNAMICS; STATES;

D O I：

10.2140/apde.2020.13.1099

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the initial-value problem for the one-dimensional nonlinear Schrodinger equation in the presence of an attractive delta potential. We show that for sufficiently small initial data, the corresponding global solution decomposes into a small solitary wave plus a radiation term that decays and scatters as t -> infinity. In particular, we establish the asymptotic stability of the family of small solitary waves.

引用

页码：1099 / 1128

页数：30

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