Solitons and soliton interactions in repulsive spinor Bose–Einstein condensates with nonzero background
Solitons and soliton interactions in repulsive spinor Bose–Einstein condensates with nonzero background
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DOI：
10.1140/epjp/s13360-021-02050-2
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发表时间：
2021-04
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影响因子：
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通讯作者：
Asela Abeya;B. Prinari;G. Biondini;P. Kevrekidis
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作者：
Asela Abeya;B. Prinari;G. Biondini;P. Kevrekidis
利用非线性薛定谔（NLS）型耦合演化方程系统的特殊约化表示，刻画了描述一维自旋为1的排斥玻色-爱因斯坦凝聚动力学的NLS型耦合演化方程系统的孤子解及其相互作用.具体来说，我们详细研究的情况下，解决方案往往在空间无限大的非零背景。首先，我们推导出一个紧凑的表示的多孤子解的系统使用逆散射变换（IST）。我们引入了解的标准形的概念，对应于背景与恒等式成比例的情形。我们发现，解决方案的渐近行为在无穷远不成比例的身份，被称为在非规范形式，可以减少到规范形式的酉变换，保持对称性的解决方案（物理上对应于复杂的旋转的量子化轴）。然后，我们给出了一个完整的表征在这个问题中产生的两个家庭的一个孤立子的解决方案，对应于铁磁和系统的极性状态，我们讨论了如何为每个家庭的孤立子的物理参数有关的光谱数据在IST。我们还表明，任何铁磁单孤子解的规范形式可以减少到一个单一的标量NLS方程的暗孤子，和任何极性单孤子解的规范形式是酉等价于一对相反的极化位移标量暗孤子的量子化轴的旋转。最后，我们讨论了两个孤立子的相互作用，我们提出了一个完整的分类可能出现的情况下，取决于是否孤立子是铁磁或极性类型。
We characterize the soliton solutions and their interactions for a system of coupled evolution equations of nonlinear Schrödinger (NLS) type that models the dynamics in one-dimensional repulsive Bose–Einstein condensates with spin one, taking advantage of the representation of such model as a special reduction of amatrix NLS system. Specifically, we study in detail the case in which solutions tend to a nonzero background at space infinities. First we derive a compact representation for the multi-soliton solutions in the system using the Inverse Scattering Transform (IST). We introduce the notion of canonical form of a solution, corresponding to the case when the background asis proportional to the identity. We show that solutions for which the asymptotic behavior at infinity is not proportional to the identity, referred to as being in non-canonical form, can be reduced to canonical form by unitary transformations that preserve the symmetric nature of the solution (physically corresponding to complex rotations of the quantization axes). Then we give a complete characterization of the two families of one-soliton solutions arising in this problem, corresponding to ferromagnetic and to polar states of the system, and we discuss how the physical parameters of the solitons for each family are related to the spectral data in the IST. We also show that any ferromagnetic one-soliton solution in canonical form can be reduced to a single dark soliton of the scalar NLS equation, and any polar one-soliton solution in canonical form is unitarily equivalent to a pair of oppositely polarized displaced scalar dark solitons up to a rotation of the quantization axes. Finally, we discuss two-soliton interactions and we present a complete classification of the possible scenarios that can arise depending on whether either soliton is of ferromagnetic or polar type.