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

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: Schr?dinger 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: Schr?dinger 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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