Optical solitons of a perturbed Biswas-Milovic equation with parabolic-law nonlinearity and spatio-temporal dispersion

Abstract

Abstract This paper deals with a new variant of the Biswas-Milovic equation, referred to as the perturbed Biswas-Milovic equation with parabolic-law nonlinearity in spatio-temporal dispersion. To our best knowledge, the considered equation which models the pulse propagation in optical fiber is studied for the first time, and the abundant optical solitons are successfully obtained utilizing the auxiliary equation method. Furthermore, we also investigate the impact of the parameters such as the spatio-temporal dispersion and the parabolic nonlinearity on the behavior of the soliton. The auxiliary equation method was employed due to its effectiveness in extracting abundant and diverse kinds of soliton solutions, including bright, kink, and singular. It has been tested and verified using Mathematica that all solutions obtained satisfy the main equation. 3D, 2D, and contour graphs of the solution functions are plotted and interpreted to understand the physical behavior of the model. The new model and findings may contribute to the understanding and characterization of the nonlinear behavior of pulse propagation in optical fibers, which is crucial for the development of optical communication systems.