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

Yi-Xiang Chen, Xiao Xiao, Zhen-Lin Mei
2020 Results in Physics  
Please cite this article as: Chen, Y-X., Xiao, X., Mei, Z-L., Optical soliton solutions of the (1+1)-dimensional space-time fractional single and coupled nonlinear Schrödinger equations, Results in Physics (2020), doi: https:// Abstract 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
more » ... 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.
doi:10.1016/j.rinp.2020.103211 fatcat:jvqv4arkazbzjokaqdhbohcad4