Diversity of solitary wave structures in Kerr media: Analyzing the complex paraxial wave equation in fiber optic communication systems

This study explores the paraxial nonlinear Schrödinger equation in Kerr media, a key model for optical fiber systems. Complex wave transformations reduce the model to a nonlinear ODE, enabling the generation of diverse solutions: bright, dark, bright-dark, and combined solitons, alongside periodic, hyperbolic, and exponential wave structures. Three novel techniques, namely the modified Riccati extended simple equation, the modified generalized exponential rational function, and the multivariate generalized exponential rational integral function methods, are used to find the solutions. Using symbolic computation tools like Mathematica, the generated soliton solutions have been confirmed by substituting them back into various relevant systems. Moreover, a variety of figures as well as their dynamics are included for the different parametric values. The proposed methods offer efficient and reliable approximations, demonstrating their utility for exploring complex nonlinear wave propagation and advancing higher-dimensional nonlinear science.