On the optical soliton solutions of Kundu–Mukherjee–Naskar equation via two different analytical methods

Abstract

We introduce optical soliton solutions of the Kundu–Mukherjee–Naskar (KMN) equation by using the Sardar subequation (SSM) and the new Kudryashov methods (nKM). The KMN equation plays an important role in modeling the fiber pulse in optics, the rogue waves in the oceans and the bending of the light beam. In order to motivate and contribute to researchers working in these fields, we focus on new solutions for the KMN model in fiber pulse transmission by utilizing the Sardar subequation and recently presented New Kudryashov technique. To reach our goal, firstly, the KMN equation has been converted to a nonlinear ordinary differential equation (NODE), then in accordance with the definitions of the proposed methods the solution sets and the solution functions have been obtained. To simulate the new solutions we have obtained and make them more understandable, the topological, anti-topological, periodic,singular and periodic soliton solutions and their properties are presented by 3D and 2D graphics. According to our literature research, these two methods that we are working on have not been applied to the KMN equation before, and we believe that the new solutions we have obtained will be useful to researchers working in modeling in this field.