Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes

被引：5

作者：

Rialland, Guillaume ^{[1
]}

机构：

[1] Univ Paris Saclay, UVSQ, CNRS, Lab Math Versailles, F-78000 Versailles, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2024年 / 241卷

关键词：

Nonlinear dispersive equations; Nonlinear Schrodinger equation; Solitary waves; Asymptotic stability; GROUND-STATES; OPERATORS; DYNAMICS;

D O I：

10.1016/j.na.2023.113474

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider perturbations of the one-dimensional cubic Schrodinger equation, under the form 𝑖� 𝜕�𝑡�𝜓� + 𝜕� 2 𝑥� 𝜓� + |𝜓�| 2 𝜓� - 𝑔�(|𝜓�| 2 )𝜓� = 0. Under hypotheses on the function 𝑔� that can be easily verified in some cases, we show that the linearized problem around a solitary wave does not have internal mode (nor resonance) and we prove the asymptotic stability of these solitary waves, for small frequencies

引用

页数：30

共 21 条

[1]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313

[2] 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

[3]

Cazenave T, 2003, Courant Lect. Notes Math., V10

[4] Spectra of linearized operators for NLS solitary waves [J].

Chang, Shu-Ming ;

Gustafson, Stephen ;

Nakanishi, Kenji ;

Tsai, Tai-Peng .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 39 (04) :1070-1111

[5] A DEGENERATE EDGE BIFURCATION IN THE 1D LINEARIZED NONLINEAR SCHRODINGER EQUATION [J].

Coles, Matt ;

Gustafson, Stephen .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (06) :2991-3009

[6]

Collot C, 2023, Arxiv, DOI arXiv:2306.03668

[7] On Selection of Standing Wave at Small Energy in the 1D Cubic Schrodinger Equation with a Trapping Potential [J].

Cuccagna, Scipio ;

Maeda, Masaya .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2022, 396 (03) :1135-1186

[8] A SURVEY ON ASYMPTOTIC STABILITY OF GROUND STATES OF NONLINEAR SCHRODINGER EQUATIONS II [J].

Cuccagna, Scipio ;

Maeda, Masaya .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2021, 14 (05) :1693-1716

[9] Quadratic Klein-Gordon equations with a potential in one dimension [J].

Germain, Pierre ;

Pusateri, Fabio .

FORUM OF MATHEMATICS PI, 2022, 10

[10] STABILITY THEORY OF SOLITARY WAVES IN THE PRESENCE OF SYMMETRY .1. [J].

GRILLAKIS, M ;

SHATAH, J ;

STRAUSS, W .

JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 74 (01) :160-197

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