Exploring Solutions' Families of the Fractional Hirota-Satsuma Coupled KdV Equation via Extended Direct Algebraic Method

Abstract

An extended direct algebraic method is used in this work to examine the soliton solutions of the fractional Hirota-Satsuma coupled Korteweg-de Vries equation. Understanding the dynamic behaviour of solitons in nonlinear systems using analytical solutions is our goal. To obtain precise soliton solutions, we utilise a logistic technique. These solutions are then shown graphically in three dimensions, two dimensions, and contours. Soliton interactions' complex dynamics and stability in fractional nonlinear systems are demonstrated by the results. This study clarifies the underlying dynamics and possible uses of soliton behaviour in complex systems, advancing our understanding of this phenomenon.