Spikes in Two-component Systems of Nonlinear Schrodinger Equations with Trapping Potentials
Spikes in Two-component Systems of Nonlinear Schrodinger Equations with Trapping Potentials
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DOI：
10.1016/j.jde.2005.12.011
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发表时间：
2006-10
影响因子：
2.4
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
最近，具有陷阱势的非线性薛定谔方程的两组分系统已经众所周知地描述了被称为双凝聚的玻色-爱因斯坦凝聚的二元混合物。在双凝聚体中，种间散射长度和陷阱势会影响尖峰的位置，使得尖峰的相互作用变得复杂，尖峰的位置难以确定。在这里，我们通过分析具有陷阱势的非线性薛定谔方程的两组分系统的最小能量（基态）解来研究双凝聚体的尖峰。我们的数学论证可以证明陷阱势和种间散射长度如何影响尖峰的位置。我们利用Nehari流形构造最小能量解，并利用奇异摄动问题的一些技巧得到它们的渐近性态。
Recently, two-component systems of nonlinear Schrödinger equations with trap potentials have been well-known to describe a binary mixture of Bose–Einstein condensates called a double condensate. In a double condensate, the locations of spikes can be influenced by the interspecies scattering length and trap potentials so the interaction of spikes becomes complicated, and the locations of spikes are difficult to be determined. Here we study spikes of a double condensate by analyzing least energy (ground state) solutions of two-component systems of nonlinear Schrödinger equations with trap potentials. Our mathematical arguments may prove how trap potentials and the interspecies scattering length affect the locations of spikes. We use Nehari's manifold to construct least energy solutions and derive their asymptotic behaviors by some techniques of singular perturbation problems.