Dynamical study of optical soliton solutions for the truncated M−fractional Kuralay-II equation via improved analytical approach

In this paper, a novel exact optical soliton solution of the Kuralay-II (K-II) equation is built based on the truncated M−fractional derivative utilizing the improved modified Sardar sub-equation method (IMSSEM). Moreover, this work’s most important feature is the use of the IMSSEM to investigate several solutions for this specific model. The main objective of this work is to explore novel and distinct soliton solutions, as well as to assess graphical representations. The most sophisticated versions of these solutions will naturally appear as rational, exponential, hyperbolic, and trigonometric functions. Finally, this new technique broadens the scope of analytical solutions, whilst the new mathematical relations provide the precise real-world scenario for comprehending the extent and applicability of the K-II equation. These explicit and closed-form solutions are thoroughly and carefully weighted, providing keen insights into the complex nature of physical phenomena occurring in various domains such as plasma physics, fluid dynamics, and optical fiber communications systems, among many others described by the K-II equations. Furthermore, the new solutions are graphed against coordinates. Structures that include various rogue waves are achieved in this paper. The findings of this investigation also demonstrate that the suggested technique is a helpful strategy to generate stable, appropriate, meaningful, and acceptable analytical solutions to various forms of nonlinear evaluation equations in mathematical physics and engineering.