Highly dispersive optical solitons in fiber Bragg gratings with cubic quadratic nonlinearity using improved modified extended tanh-function method

Abstract

This study investigates optical solitons and other traveling wave solutions in fiber Bragg gratings for coupled nonlinear Schrödinger equations with cubic quadratic nonlinearity using the improved modified extended tanh-function method (IMETFM). We discover a highly dispersive solitons in fiber Bragg such as bright solitons, dark solitons, combo bright–dark solitons and singular solitons. Moreover, we obtain hyperbolic solutions, combo hyperbolic solutions, combo periodic solutions, singular periodic solutions, rational solutions, exponential solutions, and Jacobi elliptic solutions. By comparing our obtained travelling wave solutions with existing literature, we demonstrate their novelty and substantive contribution to current research. The success of our approach suggests its potential applicability to address various nonlinear challenges in different fields, particularly within soliton theory, since the analyzed model appears in a multitude of applications. These findings are of great significance for the further development of optical communication systems. Additionally, the physical meaning of the geometrical structures for some solutions is discussed for different choices of the free parameters. It is important to mention that our proposed method is highly effective, consistent, and impactful and can be utilized to solve different physical models.