Orbital Stability of Bound States of Semiclassical Nonlinear Schrödinger Equations with Critical Nonlinearity
Orbital Stability of Bound States of Semiclassical Nonlinear Schrödinger Equations with Critical Nonlinearity
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DOI：
10.1137/070683842
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发表时间：
2008-04
期刊：
影响因子：
--
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
研究了具有临界非线性和陷阱势的半经典非线性薛定谔方程单尖峰束缚态的轨道稳定性。由于陷阱势的影响，我们导出了渐近展开式，得到了单尖峰束缚态轨道稳定性和不稳定性的必要条件。我们的论点是适用于两个组件系统的非线性薛定谔方程与一个共同的陷阱潜力，立方非线性在两个空间维度。研究了这类系统的尖峰束缚态的轨道稳定性。我们的结果表明在二维玻色-爱因斯坦凝聚中存在稳定的尖峰。
We consider the orbital stability of single-spike bound states of semiclassical nonlinear Schrodinger equations with critical nonlinearity and a trap potential. Due to the effect of the trap potential, we derive the asymptotic expansion formulas and obtain the necessary conditions for orbital stability and instability of single-spike bound states. Our argument is applied to two-component systems of nonlinear Schrodinger equations with a common trap potential, cubic nonlinearity in two spatial dimensions. The orbital stability of bound states with spikes of these systems is investigated. Our results show the existence of stable spikes in two-dimensional Bose–Einstein condensates.