Advanced techniques for analyzing solitary wave solutions of the generalized fractional Kundu-Mukherjee-Naskar model

Abstract

In this paper, five mathematical methods are used to establish solitary wave solutions for the Generalized Fractional Kundu-Mukherjee-Naskar (gFKMN) model. This model has many applications in optical fibers and communications system to describe the pulse propagation. The main motivation of this research work is to construct diverse novel results in the form of trigonometric, hyperbolic, rational and exponential functions, having fruitful applications in mathematical physics. For the physical phenomena, some solutions are plotted graphically in two-dimensional and three-dimensional by assigning specific values to the parameters under the constrain conditions on each solution with the assistance of computational software that is Mathematica 13.0. Our proposed techniques are simple and effective instruments for creating traveling wave solutions for NLPDEs. Hence this work's inventiveness is demonstrated by the application of many types of new solutions and newly employed creative ways. This facilitates additional research into nonlinear models that realistically capture important physical processes in daily life.