Exploring dynamics of multi-peak and breathers-type solitary wave solutions in generalized higher-order nonlinear Schrödinger equation and their optical applications

This paper investigates the dynamics of soliton interactions in higher-order nonlinear Schrödinger equation, which are commonly used to model multimode wave propagation in various physical scenarios, including nonlinear optics and shallow water. We constructed new exact solitary solutions in generalized forms of generalized higher-order nonlinear Schrödinger equation by using the extended generalized Riccati equation mapping method through symbolic computation. These wave solutions play a crucial role in engineering and various applied sciences. By assigning appropriate values to certain parameters in these solutions, novel graphical structures are generated, enhancing our understanding of the underlying physical phenomena in this model. These solutions shed light on the complex physical phenomena described by this dynamical model, and our computational approach is demonstrated to be simple, versatile, powerful, and effective. Furthermore, this method can also be applied to solve other complex higher-order NLSEs encountered in mathematical physics.