Optical Solitons and Other Solutions to the (2+1)-Dimensional Cubic Nonlinear Schrödinger Equation with Fractional Temporal Evolution

Abstract

In this study, the (2+1)-dimensional cubic nonlinear Schrödinger equation with fractional temporal evolution is investigated by using the extended sinh-Gordon equation expansion method. The idea of conformable fractional derivative is used in transforming the complex nonlinear partial differential equation to nonlinear ordinary differential equation. Dark, bright, mixed dark-bright, singular, mixed singular solitons and singular periodic wave solutions are successfully reached. The parametric conditions for the existence of valid solitons are given. The 2D and 3D graphics to some of the reported solutions are plotted.