Optical soliton solutions of the (1+1)-dimensional space-time fractional single and coupled nonlinear Schrödinger equations

Results in Physics

Xiao Xiao¹  Yi-Xiang Chen²  Zhen-Lin Mei³ 

[1] School of Electronics Information, Zhejiang University of Media and Communications, Hangzhou, 310018, P.R.China;Corresponding author.;School of Electronics Information, Zhejiang University of Media and Communications, Hangzhou, 310018, P.R.China;

关键词: Fractional optical soliton solutions;    Fractional nonlinear Schrödinger equation;    Coupled fractional nonlinear Schrödinger equation;    Fractional double function method;    Mittag-Leffler function;   

DOI  :  

来源: DOAJ

【 摘 要 】

The fractional double function method has been proposed to derive fractional soliton solutions and other fractional solutions of fractional nonlinear models. We find a unified solution constructed by the Mittag-Leffler function in this method, and this unified solution covers the generalized trigonometric function and hyperbolic function solutions in previous literatures. Based on this unified solution with the Mittag-Leffler function, we construct abundant solutions of the (1+1)-dimensional space-time fractional single and coupled nonlinear Schrödinger equations. From this unified solution, we find that the fractional soliton is similar to the few-cycle pulse shape and combined bright and dark soliton, and discuss their properties with the changing values of fractional order.

【 授权许可】

Unknown