不等色散系数耦合非线性薛定谔方程中的暗-亮孤子
Dark-bright solitons in coupled nonlinear Schrödinger equations with unequal dispersion coefficients
摘要：
研究了具有相等立方相互作用和不同色散系数的两组分非线性薛定谔系统.我们考虑在一个分量中有暗孤波的状态。将其视为冻结的，我们探讨了在另一个分量中形成亮孤子结构的可能性。我们确定的分歧点，在这些国家出现在明亮的组成部分的线性极限，并探讨其延续到非线性制度。一个额外的分析听话的限制被发现是消失的明亮的组件的色散。我们数值识别制度的潜在的稳定性，不仅是单峰基态（暗亮孤子），但也有一个或多个零交叉在明亮的组件的激发态。当状态被确定为不稳定的，直接数值模拟被用来调查的不稳定发展的结果。虽然我们的主要重点是在均匀设置，我们也简要地触及违反直觉的影响的潜在存在的抛物线陷阱的状态感兴趣。
英文摘要：
We study a two-component nonlinear Schr{ö}dinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright-solitonic structures in the other component. We identify bifurcation points at which such states emerge in the bright component in the linear limit and explore their continuation into the nonlinear regime. An additional analytically tractable limit is found to be that of vanishing dispersion of the bright component. We numerically identify regimes of potential stability, not only of the single-peak ground state (the dark-bright soliton), but also of excited states with one or more zero crossings in the bright component. When the states are identified as unstable, direct numerical simulations are used to investigate the outcome of the instability development. Although our principal focus is on the homogeneous setting, we also briefly touch upon the counterintuitive impact of the potential presence of a parabolic trap on the states of interest.
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