混合N耦合非线性薛定谔方程中的非线性暗孤子及其碰撞
Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schrödinger equations
摘要：
利用Hirota的双线性化方法，得到了具有混合符号的聚焦和散焦型非线性系数的可积N耦合非线性Schr{<$}dinger（CNLS）方程的混合型（明-暗）孤子解.对于混合N-CNLS方程，一般可以用$(N-1)$方法分裂明孤子和暗孤子。通过系统地分析这些耦合亮、暗孤子的碰撞动力学，指出对于$N>2$，如果亮孤子出现在至少两个分量中，则在碰撞过程中亮孤子会出现强度重新分布、振幅相关相移和相对分离距离变化等非平凡效应。然而，它们的对应物，暗孤子，经历弹性碰撞，但经历相同的振幅相关的相移的亮孤子。因此，在混合CNLS系统中，亮孤子的形变碰撞和暗孤子的弹性碰撞以及振幅相关的相移同时存在，两者之间存在着复杂的相互影响。
英文摘要：
Mixed type (bright-dark) soliton solutions of the integrable N-coupled nonlinear Schr{ö}dinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients are obtained by using Hirota's bilinearization method. Generally, for the mixed N-CNLS equations the bright and dark solitons can be split up in $(N-1)$ ways. By analysing the collision dynamics of these coupled bright and dark solitons systematically we point out that for $N>2$, if the bright solitons appear in at least two components, non-trivial effects like onset of intensity redistribution, amplitude dependent phase-shift and change in relative separation distance take place in the bright solitons during collision. However their counterparts, the dark solitons, undergo elastic collision but experience the same amplitude dependent phase-shift as that of bright solitons. Thus in the mixed CNLS system there co-exist shape changing collision of bright solitons and elastic collision of dark solitons with amplitude dependent phase-shift, thereby influencing each other mutually in an intricate way.
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