Spikes in two coupled nonlinear Schrödinger equations
Spikes in two coupled nonlinear Schrödinger equations
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DOI：
10.1016/j.anihpc.2004.03.004
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发表时间：
2005-07
影响因子：
1.9
通讯作者：
Tai-Chia Lin;Juncheng Wei
中科院分区：
文献类型：
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作者：
Tai-Chia Lin;Juncheng Wei
本文通过分析两个耦合非线性Schrödinger方程的最小能量解，研究了双凝聚态中峰态的相互作用和组态。当种间散射长度为正且足够大时，双凝聚体的尖峰相互排斥，表现为两个独立的尖峰。相反，当种间散射长度为负且足够大时，双凝聚体的峰相互吸引并表现为单峰。我们的数学论证可以证明这样的物理现象。首先利用Nehari流形构造最小能量解，然后利用奇异摄动问题的一些技巧推导出最小能量解的渐近性质。结果表明，相互作用项决定了两个峰值的位置和最小能量解的渐近形状。
Here we study the interaction and the configuration of spikes in a double condensate by analyzing least energy solutions of two coupled nonlinear Schrödinger equations which model Bose–Einstein condensates of two different hyperfine spin states. When the interspecies scattering length is positive and large enough, spikes of a double condensate repel each other and behave like two separate spikes. In contrast, spikes of a double condensate attract each other and behave like a single spike if the interspecies scattering length is negative and large enough. Our mathematical arguments can prove such physical phenomena. We first use Nehari's manifold to construct least energy solutions, and then use some techniques of singular perturbation problems to derive the asymptotic behavior of least energy solutions. It is shown that the interaction term determines the locations of the two spikes and the asymptotic shape of least energy solutions.