一类非齐次非线性 Schrödinger 方程驻波的轨道稳定性

数学物理学报 ›› 2024, Vol. 44 ›› Issue (2): 476-483.

一类非齐次非线性 Schrödinger 方程驻波的轨道稳定性

刘鑫艳(),李晓光^*()

四川师范大学数学科学学院 & 可视化计算与虚拟现实四川省重点实验室成都 610066

收稿日期:2023-03-22 修回日期:2023-10-25 出版日期:2024-04-26 发布日期:2024-04-07
通讯作者: * 李晓光, Email:lixgmath@163.com
作者简介:刘鑫艳, Email:liuxinyanyyy@163.com
基金资助:
国家自然科学基金(11771314)

Orbital Stability of Standing Waves for a Class of Inhomogeneous Nonlinear Schrödinger Equation

Liu Xinyan(),Li Xiaoguang^*()

School of Mathematical Science and V.C. & V.R. Key Lab, Sichuan Normal University, Chengdu 610066

Received:2023-03-22 Revised:2023-10-25 Online:2024-04-26 Published:2024-04-07
Supported by:
NSFC(11771314)

摘要/Abstract

摘要：

该文主要研究一类非齐次非线性 Schrödinger 方程在质量次临界条件下驻波的存在性和轨道稳定性. 通过一个变分原理, 讨论了约束变分问题极小化序列的紧性, 并由此得到驻波的存在性, 进一步证明了驻波的轨道稳定性.

关键词: 极小化序列, 紧性, 驻波的轨道稳定性

Abstract:

In this paper, we study the existence and orbital stability of standing waves for a class of nonhomogeneous nonlinear Schrödinger equations under mass subcritical conditions. By means of a variational principle, we discuss the compactility of minimization sequence of constrained variational problems. From this, we obtain the existence of standing waves and prove the orbital stability of standing waves.

Key words: Minimization sequence, Compactness, Orbital stability of standing waves

中图分类号:

O175.2

刘鑫艳, 李晓光. 一类非齐次非线性 Schrödinger 方程驻波的轨道稳定性[J]. 数学物理学报, 2024, 44(2): 476-483.

Liu Xinyan, Li Xiaoguang. Orbital Stability of Standing Waves for a Class of Inhomogeneous Nonlinear Schrödinger Equation[J]. Acta mathematica scientia,Series A, 2024, 44(2): 476-483.

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