Complex and Real Optical Soliton Properties of the Paraxial Non-linear Schrodinger Equation in Kerr Media With M-Fractional

Abstract

In this paper, we use the modified exponential function method in terms of K-f(x) instead of e(f(x))and the extended sinh-Gordon method to find some new family solution of the M-fractional paraxial non-linear Schrodinger equation. The novel complex and real optical soliton solutions are plotted in 2-D, 3-D with a contour plot. Moreover, the dark exact solutions, singular soliton solutions, kink-type soliton solution, and periodic dark-singular soliton solutions for M-fractional paraxial non-linear Schrodinger equation are constructed. We guarantee that all solutions are new and verified the main equation of the M-fractional paraxial wave equation. For existence, the constraint condition is also added.