Optical solitons in Fiber Bragg Gratings for the coupled form of the nonlinear [formula omitted]-dimensional Kundu-Mukherjee-Naskar equation via four powerful techniques

Abstract

In this article, four powerful techniques namely, the three wave method, double exponential, homoclinic breather, M-Shaped rational, M-Shaped with one kink, and M-Shaped with two kink are putting into practice to bolster the new optical solutions of the coupled form of the nonlinear (2+1)-dimensional Kundu-Mukherjee-Naskar equation in Fiber Bragg Gratings (FBGs). Implementation of the appropriate functions of the solutions results in a different form of multi-wave solutions with their interaction phenomena such as dark soliton solutions, singular soliton solutions, bright soliton solutions, kink soliton solutions, Multi-Peak soliton solutions, multi dark-bright soliton solutions, multi bright soliton solutions, multi dark soliton solutions with different structure, multi M-Shaped soliton solutions, multi M-Shaped soliton solutions, M-Shaped soliton solutions with different structure, kink soliton solutions with different structure, and periodical M-Shaped soliton solutions. Three-dimensional graphics demonstrating the dependability and productivity of the suggested methodologies are used to describe the dynamics of the produced solutions.