On new diverse variety analytical optical soliton solutions to the perturbed nonlinear Schrödinger equation

Abstract

This study focuses on investigating the optical soliton solutions for the perturbed nonlinear Schrödinger equation involving Kerr nonlinearity. It should be noted that the non-integrable nature of the nonlinear Schrödinger equation becomes apparent when the Kerr law nonlinearity is absent. This absence of integrability significantly obstructs finding exact solutions. Our research utilizes an innovative analytical technique, the modified generalized exponential rational function method, to derive new soliton solutions. The new soliton solutions we obtained are quite versatile and practical for real-world applications. They are expressed in terms of elementary functions such as exponentials, trigonometric functions, and hyperbolic functions. This simplicity allows for easy comprehension and straightforward utilization in various scenarios. We present a variety of visualizations and graphs to enhance the understanding of the physical behaviors exhibited by the new soliton solutions. The graphical outcomes give insights into soliton evolution and dynamics under various conditions. Our study shows the analytical technique’s efficacy in producing new soliton solutions for the perturbed nonlinear Schrödinger equation. We explore the possibility of expanding the method to discover solutions for alternative nonlinear partial differential equations that arise within soliton theory and nonlinear optics. The analytical approach offers a systematic framework for obtaining new soliton solutions for a broad class of nonlinear wave equations. Our employed methodologies hold also the potential to significantly advance the field and contribute to the development of new methodologies for tackling these challenging equations.