多分量相干耦合和非相干耦合孤子及其碰撞
Multicomponent coherently coupled and incoherently coupled solitons and their collisions
摘要：
本文研究克尔型非线性介质中多场同时传输的可积多分量相干耦合非线性薛定谔方程。采用非标准型Hirota双线性化方法，得到了$m$ -CCNLS方程的正确双线性方程，并得到了更一般的单峰和双峰亮孤子，包括特殊的平顶亮孤子.孤子被分为相干耦合孤子和非相干耦合孤子取决于相干非线性的存在和不存在，由于存在的共同传播模式/组件。此外，通过获得更一般的两个孤子的解决方案，使用这种非标准的双线性化方法，我们表明，相干耦合孤子和非相干耦合孤子之间的碰撞显示出非平凡的碰撞行为，其中前者总是经历能量切换伴随着振幅相关的相移和相对分离距离的变化，离开后者不变。而相干耦合孤子之间的碰撞则是标准的弹性碰撞。我们的研究还揭示了一个重要的事实，即在含有$m=2$的$m$-CCNLS系统中产生的非相干耦合孤子之间的碰撞总是弹性的，而对于$m>2$，碰撞变得复杂，并且对于这种情况，$m$ -CCNLS系统表现出有趣的孤子能量共享碰撞，其特征在于强度重新分布。振幅相关的相移和相对分离距离的变化，这是类似的多分量Manakov孤子碰撞。这表明，除了Manakov系统之外，$m$ -CCNLS系统也可以是基于孤子碰撞的光学计算的合适候选者。
英文摘要：
We consider the integrable multicomponent coherently coupled nonlinear Schrödinger (CCNLS) equations describing simultaneous propagation of multiple fields in Kerr type nonlinear media. The correct bilinear equations of $m$-CCNLS equations are obtained by using a non-standard type of Hirota's bilinearization method and the more general bright one solitons with single hump and double hump profiles including special flat-top profiles are obtained. The solitons are classified as coherently coupled solitons and incoherently coupled solitons depending upon the presence and absence of coherent nonlinearity arising due to the existence of the co-propagating modes/components. Further, by obtaining the more general two-soliton solutions using this non-standard bilinearization approach we demonstrate that the collision among coherently coupled soliton and incoherently coupled soliton displays a non-trivial collision behaviour in which the former always undergoes energy switching accompanied by an amplitude dependent phase-shift and change in the relative separation distance, leaving the latter unaltered. But the collision between coherently coupled solitons alone is found to be standard elastic collision. Our study also reveals the important fact that the collision between incoherently coupled solitons arising in the $m$-CCNLS system with $m=2$ is always elastic, whereas for $m>2$ the collision becomes intricate and for this case the $m$-CCNLS system exhibits interesting energy sharing collision of solitons characterized by intensity redistribution, amplitude dependent phase-shift and change in relative separation distance which is similar to that of the multicomponent Manakov soliton collisions. This suggests that the $m$-CCNLS system can also be a suitable candidate for soliton collision based optical computing in addition to the Manakov system.
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