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This paper investigates the resonant nonlinear Schrödinger equation (RNSE) with parabolic law nonlinearity, modeling optical pulse propagation in nonlinear optical fibers. By employing the Kumar–Malik approach, we have derived some analytical soliton solutions for the considered equation. These solutions are in the form of Jacobi elliptic, hyperbolic, trigonometric, exponential functions are obtained by this analytical approach. Dark, bright, singular, and periodic wave solitons are created by selecting proper values for the parameters. The new results are compared with previously obtained results. In addition, the physical properties of the presented solutions are represented by 2d, contour and 3d graphs created by selecting appropriate constant parameters. The findings of this study are novel. The acquired results highlight the simplicity, efficacy, and dependability of this method in the analysis of various nonlinear models encountered in the fields of mathematical physics and engineering.
Sağlam et al. (Mon,) studied this question.