$N$耦合非线性薛定谔系统中的多峰非简并基亮孤子
Multihumped nondegenerate fundamental bright solitons in $N$-coupled nonlinear Schrödinger system
摘要：
本文研究了Manakov型耦合多分量非线性薛定谔方程非退化基本亮孤子解的存在性。为了得到这类非退化矢量孤子解，我们采用了Hirota双线性方法和适当的一般种子解。非常有趣的是，所获得的$N$耦合非线性薛定谔（CNLS）系统的非简并基本孤子解允许多峰自然强度分布。我们明确地证明了这一特性，考虑非简并孤子解的$3$和$4$ -CNLS系统。通过对已得到的完全非简并孤子解的波数施加适当的限制，我们还指出了一类特殊的部分非简并孤子解的存在性.这类孤子解也可以表现出多峰轮廓结构。最后，以$3$ -CNLS系统为例，给出了非简并基本孤子的稳定性分析.数值计算结果证实了三峰轮廓在5%和10%白噪声扰动下的稳定性。非简并基孤子解的多峰特性将在多模光纤中增强数据流的多级光通信应用中发挥重要作用。
英文摘要：
In this letter we report the existence of nondegenerate fundamental bright soliton solution for coupled multi-component nonlinear Schrödinger equations of Manakov type. To derive this class of nondegenerate vector soliton solutions, we adopt the Hirota bilinear method with appopriate general class of seed solutions. Very interestingly the obtained nondegenerate fundamental soliton solution of the $N$-coupled nonlinear Schrödinger (CNLS) system admits multi-hump natured intensity profiles. We explicitly demonstrate this specific property by considering the nondegenerate soliton solutions for $3$ and $4$-CNLS systems. We also point out the existence of a special class of partially nondegenerate soliton solutions by imposing appropriate restrictions on the wavenumbers in the already obtained completely nondegenerate soliton solution. Such class of soliton solutions can also exhibit multi-hump profile structures. Finally, we present the stability analysis of nondegenerate fundamental soliton of the $3$-CNLS system as an example. The numerical results confirm the stability of triple-humped profile nature against perturbations of 5\% and 10\% white noise. The multi-hump nature of nondegenerate fundamental soliton solution will be usefull in multi-level optical communication applications with enhanced flow of data in multi-mode fibers.
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