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

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 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.

Keywords

• Fractional optical soliton solutions
• Fractional nonlinear Schrödinger equation
• Coupled fractional nonlinear Schrödinger equation
• Fractional double function method
• Mittag-Leffler function