Variational problems for the system of nonlinear Schrödinger equations with derivative nonlinearities

被引：0

作者：

Hirayama, Hiroyuki ^{[1
]}

Ikeda, Masahiro ^{[2
,3
]}

机构：

[1] Univ Miyazaki, Fac Engn, 1-1 Gakuenkibanadai Nishi, Miyazaki 8892192, Japan

[2] Keio Univ, Fac Sci & Technol, Dept Math, Nihonbashi 1 Chome Mitsui Bldg,15th floor,1-4-1 Ni, Tokyo 1030027, Japan

[3] RIKEN, Ctr Adv Intelligence Project, Tokyo, Japan

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2024年 / 63卷 / 07期

基金：

日本学术振兴会;

关键词：

35Q55; 35A01; 35A15; 35B35; SOLITARY WAVES; ORBITAL STABILITY; WELL-POSEDNESS;

D O I：

10.1007/s00526-024-02782-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem of the system of nonlinear Schr & ouml;dinger equations with derivative nonlinearlity. This system was introduced by Colin and Colin (Differ Int Equ 17:297-330, 2004) as a model of laser-plasma interactions. We study existence of ground state solutions and the global well-posedness of this system by using the variational methods. We also consider the stability of traveling waves for this system. These problems are proposed by Colin-Colin as the open problems. We give a subset of the ground-states set which satisfies the condition of stability. In particular, we prove the stability of the set of traveling waves with small speed for 1-dimension.

引用

页数：31

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