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

Abstract

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

CLC Number:

O175.23

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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References 42

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Normalized Solutions to the Schrödinger Equation with Forcing Perturbation Term

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