带强制扰动项的 Schrödinger 方程的正规化解——献给李工宝教授 70 寿辰

数学物理学报 ›› 2025, Vol. 45 ›› Issue (6): 1791-1805.

带强制扰动项的 Schrödinger 方程的正规化解——献给李工宝教授 70 寿辰

贾慧芳^*(), 叶湘怡

广东工业大学数学统计学院广州 510520

收稿日期:2025-02-05 修回日期:2025-07-25 出版日期:2025-12-26 发布日期:2025-11-18
通讯作者: 贾慧芳 E-mail:hf_jia@mails.ccnu.edu.cn
基金资助:
国家自然科学基金(12471103);广东省自然科学基金(2024A1515012370)

Normalized Solutions to the Schrödinger Equation with Forcing Perturbation Term

Huifang Jia^*(), Xiangyi Ye

School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520

Received:2025-02-05 Revised:2025-07-25 Online:2025-12-26 Published:2025-11-18
Contact: Huifang Jia E-mail:hf_jia@mails.ccnu.edu.cn
Supported by:
NSFC(12471103);Guangdong Basic and Applied Basic Research Foundation of China(2024A1515012370)

摘要/Abstract

摘要：

该文采用约束变分方法研究了带有部分束缚势和排斥扰动项的 Schrödinger 方程正规化解的存在性及其量化性质. 特别地, 涵盖了在物理上具有重要意义的三维立方-五次非线性情形, 即带有散焦五次非线性项的玻色-爱因斯坦凝聚体 (BEC) 雪茄形模型的极限情况. 进一步, 还讨论了与相关时间依赖问题对应的驻波解的稳定性.

关键词: Schrödinger 方程, 正规化解, 排斥扰动项, 稳定性

Abstract:

This paper employs the constrained variational method to study the existence and qualitative properties of the normalized solutions to the Schrödinger equation with a partially confining potential and repulsive perturbation term. Specifically, it addresses the physically significant three dimensional cubic-quintic nonlinear case, which corresponds to the limiting situation of the cigar-shaped model for Bose-Einstein condensates (BEC) with a defocusing quintic nonlinear term. Furthermore, the stability of the corresponding standing wave solutions for the related time-dependent problem is also discussed.

Key words: Schrödinger equation, normalized solution, repulsive perturbation term, stability

中图分类号:

O175.23

贾慧芳, 叶湘怡. 带强制扰动项的 Schrödinger 方程的正规化解——献给李工宝教授 70 寿辰[J]. 数学物理学报, 2025, 45(6): 1791-1805.

Huifang Jia, Xiangyi Ye. Normalized Solutions to the Schrödinger Equation with Forcing Perturbation Term[J]. Acta mathematica scientia,Series A, 2025, 45(6): 1791-1805.

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