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A model condition for the propagation of ultrashort pulses in optical fiber frameworks could be established through the extensive generalization of the nonlinear Schrödinger equation introduced by Triki and Biswas. This study uses two significant and effective trustworthy methods to examine the Triki–Biswas (TB) equation. Sardar Subequation Methods (SSM) and the generalized Kudryashov (KUD) method generate solutions for trigonometric, hyperbolic, exponential, and rational functions. These approaches are specifically designed for handling solitary wave patterns, dark-singular-mixed solitons, combined dark-bright solitons, singletons, bright solitons, exponential and rational functions, as well as periodic solitons. All of these solution classes contribute to the physical dynamics of outcomes. These findings represent an innovative extension of the soliton domain within the TB model and are being reported for the first time in our investigation. In addition, Mathematica simulations are used to display the 3D and 2D graphs to explain the identified solutions' physical dynamics. [ABSTRACT FROM AUTHOR]