Soliton solutions of the third-order perturbed nonlinear Schrödinger equation having the Kudryashov’s law of self-modulation form and modulation instability analysis

Purpose The present article is dedicated to the analytical construction of soliton solutions for the third-order perturbed nonlinear Schrödinger equation having the Kudryashov’s law of selfphase modulation form in the absence of the group velocity dispersion term. Such a formulation is especially relevant in the context of ultrashort pulse propagation through nonlinear optical media, where higher-order dispersive and nonlinear impacts dominate. Design/methodology/approach To retrieve soliton solutions, the new Kudryashov method is employed, which has been verified to be an efficient and systematic technique for solving nonlinear evolution equations. This method facilitates the reduction of the governing partial differential equation to a solvable nonlinear ordinary differential equation through an appropriate transformation. Findings The study yields both bright and dark soliton solutions. Soliton solutions obtained under this framework are expressed in closed form, and their validity is confirmed through direct substitution. Their qualitative properties and physical dynamics are explored through comprehensive visualizations, including 2-dimensional plots, contour maps, and 3-dimensional surface diagrams. Social implications text. Originality/value The results contribute to the understanding of nonlinear pulse dynamics in the absence of the group velocity dispersion term regimes and indicate the applicability and robustness of the new Kudryashov method for handling complex nonlinear models in mathematical physics and optical communication systems.