Exploring optical soliton solutions of a self-focusing nonlinear Schrödinger equation by two effective techniques

In this manuscript, we have conducted a comprehensive investigation of the self-focusing Schrödinger equation with fourth-order dispersion, yielding closed-form results for crucial optical soliton solutions. To achieve this, we have employed two distinct methodologies. Firstly, we harnessed the power of the generalized Kudryashov method to derive novel solutions for the Schrödinger equation, expanding the landscape of possible solutions. To further enrich our understanding of optical solitons, we incorporated the ( 1/𝒢^') expansion technique, uncovering additional soliton solutions. The behavior of these solutions is vividly illustrated through 2D and 3D graphical representations, shedding light on the characteristics of bright, breather-type, and combined M-W-shaped optical solitons. Moreover, we have meticulously examined the influence of specific parameters on the dynamics of soliton solutions obtained via the ( 1/𝒢^') method, providing valuable insights into the interplay between these parameters and the soliton behavior.