Abstract
In this paper, we use the modified exponential function method in terms of 𝐾𝑓(𝑥) instead of 𝑒𝑓(𝑥) and the extended sinh-Gordon method to find some new family solution of the M-fractional paraxial nonlinear 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 solution, singular soliton solutions, kink-type soliton solution and periodic dark-singular soliton solutions for M-fractional paraxial nonlinear 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.
Highlights
The breaking up and moving away from ultrashort pulses of a field related to electricity-producing magnetic fields or radiation into a medium is a multidimensional important physical phenomenon
We have the following non-linear partial differential equation (NLPDE)
In Equation (12) if ab > 0 we get elliptic non-linear Schrödinger equation and if ab < 0, Equation (12) becomes hyperbolic nonlinear Schrödinger equation
Summary
Received: 21 September 2019 Accepted: 06 November 2019 Published: 21 November 2019. We use the modified exponential function method in terms of Kf(x) instead of ef(x)and the extended sinh-Gordon method to find some new family solution of the M-fractional paraxial non-linear Schrödinger equation. The novel complex and real optical soliton solutions are plotted in 2-D, 3-D with a contour plot. The dark exact solutions, singular soliton solutions, kink-type soliton solution, and periodic dark-singular soliton solutions for M-fractional paraxial non-linear Schrödinger equation are constructed. We guarantee that all solutions are new and verified the main equation of the M-fractional paraxial wave equation.
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