Dynamic of solitary wave pulse speed with dual-power law refractive index in homogeneous optical waveguides

This paper explores the nonlinear Shrödinger equation (NLSE) with dual-power law (DPL) nonlinear terms which illustrates how the temporal fluctuations of the system parameters may be used to regulate the solitary wave speed in an in-homogeneous optical waveguide with a DPL refractive index. The main goal is to comprehend the dynamics of these short light pulses propagation in optical media with DPL nonlinearity and temporally controlled dispersion. The generalized exponential rational function (GERF) approach is employed to obtain a variety of traveling wave solutions. This method finds extensive applications in both mathematics and physics. Together with the forming conditions, the attributes for optical bright and multipeak solitons with this media are presented. The derived solutions are also presented graphically to help visualize the model’s physical processes. Many diverse similar models that arise in the applied sciences may be resolved with this method since it is believable, effective, and successful. Beyond the various models encountered in the applied sciences, this robust, strong, and efficient technique can be expanded to handle many kinds of higher-order nonlinear problems that arise in contemporary research fields.