Stable standing waves for a Schrodinger system with nonlinear χ3 response

被引：0

作者：

Colin, Mathieu ^{[1
]}

Watanabe, Tatsuya ^{[2
]}

机构：

[1] Univ Bordeaux, CNRS, Bordeaux INP, IMB,UMR 5251, F-33400 Talence, France

[2] Kyoto Sangyo Univ, Fac Sci, Dept Math, Kita Ku, Kyoto 6038555, Japan

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2023年 / 64卷 / 10期

关键词：

CONCENTRATION-COMPACTNESS PRINCIPLE; EQUATIONS; CALCULUS;

D O I：

10.1063/5.0165615

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we consider standing waves for a nonlinear Schrodinger system which appears in nonlinear optics. This two-component system contains a cubic nonlinear term which is called chi(3)-interaction, and has a strong coupling on one side only. Oliveira and Pastor [Anal. Math. Phys. 11, 123 (2021)] showed the existence of ground states solutions for the corresponding stationary problems and investigated their stability. In our study, by considering the solvability of a constraint minimization problem, we show the existence of stable standing wave solutions. We also investigate the correspondence between minimizers and ground state solutions.

引用

页数：19

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