Search

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.

In this paper, we have successfully extracted novel analytic solutions for the (1+2)-dimensional Chiral non-linear Schrödinger (NLS) equation by modified extended tanh expansion method combined with new Riccati solutions (METEM-cNRCS) as far as we know. When a wave transformation is applied to the considered Chiral NLS equation, a nonlinear ODE is obtained. Assuming the solutions of ODE have a form as the method suggests, and substituting the trial solutions to the ODE, we get a polynomial. Gathering the coefficients with the same power in the polynomial, we acquire an algebraic equation system. So, we may obtain the abundant solutions of the (1+2)-dimensional Chiral NLS equation by solving the system via Maple. The plots of some solutions are demonstrated to explain the dynamics of the solutions. It is expected that the results of the paper are a guide for future works in traveling wave theory.