Optical soliton solutions for the parabolic nonlinear Schrödinger Hirota’s equation incorporating spatiotemporal dispersion via the tanh method linked with the Riccati equation

This manuscript presents some new exact solutions for the dispersive Schrödinger Hirota’s (SH) equation considering the effects of spatio-temporal dispersion with parabolic law nonlinearity. A wave transformation technique is implemented to transform the SH equation into a nonlinear ordinary differential equation. The solutions for the dispersive SH equation are derived using the modified extended tanh approach. These solutions exhibits various sorts of solitons, including bright, dark, periodic, and singular solitons. The findings of this research hold potential significance in the domain of fiber-optic communication, as they contribute to a deeper understanding of soliton dynamics.