Optical singular and dark solitons to the (2 + 1)-dimensional time–space fractional nonlinear Schrödinger equation

Abstract

In this study, the (2+1)-dimensional nonlinear Schrödinger equation with fractional-order derivative in both time and space is considered within the modified Riemann–Liouville derivatives. This fractional-order equation is newly derived by using the fractional variational principle and the semi-inverse method. By introducing the fractional complex transform, the (G′∕G)-expansion method, the tanh–coth method, and the modified simple equation method are used to obtain the explicit analytical solutions of this equation. As a result, optical singular and dark soliton solutions are obtained. The behaviours of the soliton solutions are expressed by 2D and 3D graphs.