Optical singular and dark solitons to the (2

In this study, the (2 + 1)-dimensional nonlinear Schrodinger 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.

Automated summary

In this study, a (2 + 1)-dimensional nonlinear Schrodinger equation with fractional-order derivative was considered and newly derived using the fractional variational principle and the semi-inverse method. By introducing the fractional complex transform, explicit analytical solutions were obtained using the (G'/G)-expansion method, the tanh-coth method, and the modified simple equation method, resulting in optical singular and dark soliton solutions. The behaviors of the soliton solutions were expressed by 2D and 3D graphs.