CROSS-INVARIANT SETS OF THE COUPLED NONLINEAR SCHRÖDINGER SYSTEM WITH HARMONIC POTENTIALS

被引：0

作者：

Zhou, Xinlu ^{[1
]}

Zhang, Jian ^{[1
]}

机构：

[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2024年

基金：

中国国家自然科学基金;

关键词：

Bose-Einstein condensates; coupled nonlinear Schr & ouml; dinger system; cross-invariant sets; sharp condition; global existence; SCHRODINGER-EQUATIONS; GLOBAL EXISTENCE; SHARP THRESHOLD; SOLITARY WAVES; GROUND-STATES; BOUND-STATES; SPIKES;

D O I：

10.3934/dcdsb.2024186

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the coupled nonlinear Schr & ouml;dinger system with harmonic potentials { - i phi t = triangle phi - |x|(2)phi + mu (1)|phi|(2) phi + beta|psi|(2)phi, (t, x) is an element of R+ x R-N, - i psi t = triangle psi - |x|(2) psi + mu (2)|psi|(2)psi + beta|phi|(2) psi, (t, x) is an element of R+ x R-N, which describes the Bose-Einstein condensates under the magnetic trap. The cross-invariant sets of the evolution flow are obtained by constructing the cross constrained variational problem. Moreover, the sharp condition for global existence and blowup of the solutions is derived.

引用

页码：2729 / 2739

页数：11

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