Atas, Sibel Sehriban; Ali, Karmina K.

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.

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