Least Energy Solutions for Nonlinear Schrödinger Systems with Mixed Attractive and Repulsive Couplings
Least Energy Solutions for Nonlinear Schrödinger Systems with Mixed Attractive and Repulsive Couplings
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DOI：
10.1515/ans-2015-0101
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发表时间：
2015-02
影响因子：
1.8
通讯作者：
Yohei K. Sato;Zhi-Qiang Wang
中科院分区：
文献类型：
--
作者：
Yohei K. Sato;Zhi-Qiang Wang
本文研究了玻色-爱因斯坦凝聚模型中一类非线性椭圆型三方程组的基态解。与现有的文献中的工作已经在纯吸引或纯排斥的情况下，我们的研究集中在吸引和排斥耦合的混合相互作用的效果。我们建立了最小能量正解的存在性，并研究了基态解的渐近分布，给出了同步和分离共存的指示。特别是，我们显示对称性破缺的基态解决方案。
Abstract In this paper we study the ground state solutions for a nonlinear elliptic system of three equations which comes from models in Bose-Einstein condensates. Comparing with existing works in the literature which have been on purely attractive or purely repulsive cases, our investigation focuses on the effect of mixed interaction of attractive and repulsive couplings. We establish the existence of least energy positive solutions and study asymptotic profile of the ground state solutions, giving indication of co-existence of synchronization and segregation. In particular we show symmetry breaking for the ground state solutions.