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.
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页数：11
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