二分量非线性Schrodinger系统的半Skyrmions解和Spike涡解
Half-Skyrmions and Spike-Vortex Solutions of Two-Component Nonlinear Schrodinger Systems
摘要：
最近，已观察到整数拓扑电荷的skyrmions数值，但尚未严格显示在两个组件系统的非线性薛定谔方程（NLSE）描述的二元混合玻色-爱因斯坦凝聚。此外，在Schwinger玻色子的玻色-爱因斯坦凝聚的非线性σ模型中也可以发现具有半整数拓扑荷的半skyrmions。在这里，我们严格证明了半skyrmions的存在性，这可能来自一种新的类型的孤子解称为钉涡解决方案的两个组件的NLSE在整个平面上。这些在一个分量中具有尖峰而在另一个分量中具有涡旋的尖峰-涡旋解可以形成半skyrmions。利用Liapunov-Schmidt约化过程，我们可以得到NLSE的两组分系统的尖峰涡解。
英文摘要：
Recently, skyrmions with integer topological charges have been observed numerically but have not yet been shown rigorously on two-component systems of nonlinear Schrodinger equations (NLSE) describing a binary mixture of Bose-Einstein condensates. Besides, half-skyrmions characterized by half-integer topological charges can also be found in the nonlinear sigma model which is a model of the Bose-Einstein condensate of the Schwinger bosons. Here we prove rigorously the existence of half-skyrmions which may come from a new type of soliton solutions called spike-vortex solutions of two-component systems of NLSE on the entire plane. These spike-vortex solutions having spikes in one component and a vortex in the other component may form half-skyrmions. By Liapunov-Schmidt reduction process, we may find spike-vortex solutions of two-component systems of NLSE.
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