Diverse optical soliton solutions to the generalized resonant nonlinear Schrödinger equation through an integral method

This paper is concerned with the generalized resonant nonlinear Schrödinger equation with an arbitrary index, which describes ultra-short pulse propagation in optical fibers. The study uses the main integration method: the modified generalized Riccati equation mapping method, to construct and analyze combined forms of optical soliton solutions. The results are multifaceted, revealing a variety of optical soliton solutions, such as rational solutions in hyperbolic functions, combined solutions of hyperbolic and trigonometric functions, bright, singular, , kink-shaped, smooth kink, and periodic singular. Moreover, two-dimensional, three-dimensional, and contour graphs of some obtained optical soliton solutions are plotted to illustrate the importance of the generalized resonant nonlinear Schrödinger equation, using suitable values of physical parameters. Two-dimensional graphs are used to illustrate the dynamic behavior of the solutions, taking into account the impact of the nonlinear index n and the time parameter t. The obtained optical solutions are considered novel and most likely have not been reported in the literature before.