Journal of Advanced Research ( IF 11.4 ) Pub Date : 2021-05-18 , DOI: 10.1016/j.jare.2021.05.004 Gang-Zhou Wu 1 , Chao-Qing Dai 1 , Yue-Yue Wang 1 , Yi-Xiang Chen 2
|
Introduction
Fractional nonlinear models have been widely used in the research of nonlinear science. A fractional nonlinear Schrödinger equation with distributed coefficients is considered to describe the propagation of pi-second pulses in inhomogeneous fiber systems. However, soliton molecules based on the fractional nonlinear Schrödinger equation are hardly reported although many fractional soliton structures have been studied.
Objectives
This paper discusses the propagation and interaction between special fractional soliton and soliton molecules based on analytical solutions of a fractional nonlinear Schrödinger equation.
Methods
Two analytical methods, including the variable-coefficient fractional mapping method and Hirota method with the modified Riemann–Liouville fractional derivative rule, are used to obtain analytical non-travelling wave solutions and multi-soliton approximate solutions.
Results
Analytical non-travelling wave solutions and multi-soliton approximate solutions are derived. The form conditions of soliton molecules are given, and the dynamical characteristics and interactions between special fractional solitons, multi-solitons and soliton molecules are discussed in the periodic inhomogeneous fiber and the exponential dispersion decreasing fiber.
Conclusion
Analytical chirp-free and chirped non-traveling wave solutions and multi-soliton approximate solutions including soliton molecules are obtained. Based on these solutions, dynamical characteristics and interactions between special fractional solitons, multi-solitons and soliton molecules are discussed. These theoretical studies are of great help to understand the propagation of optical pulses in fibers.
中文翻译：
非均匀纤维中特殊分数孤子与孤子分子的传播与相互作用
介绍
分数非线性模型在非线性科学研究中得到了广泛的应用。考虑使用具有分布系数的分数非线性薛定谔方程来描述非均匀光纤系统中 pi 秒脉冲的传播。然而，尽管已经研究了许多分数孤子结构，但几乎没有报道基于分数非线性薛定谔方程的孤子分子。
目标
本文基于分数非线性薛定谔方程的解析解，讨论了特殊分数孤子与孤子分子之间的传播和相互作用。
方法
两种解析方法，包括变系数分数映射方法和具有改进的黎曼-刘维尔分数导数规则的广田方法，用于获得解析非行波解和多孤子近似解。
结果
推导出解析非行波解和多孤子近似解。给出了孤子分子的形成条件，讨论了周期性非均匀光纤和指数色散递减光纤中特殊分数孤子、多孤子和孤子分子之间的动力学特性和相互作用。
结论
得到解析无啁啾和啁啾非行波解和包含孤子分子的多孤子近似解。基于这些解，讨论了特殊分数孤子、多孤子和孤子分子之间的动力学特性和相互作用。这些理论研究对理解光脉冲在光纤中的传播有很大帮助。
京公网安备 11010802027423号