Computational analysis of soliton dynamics and their applications in the fractional Kairat-II equation

Abstract In this paper, we investigate the dynamical behaviour and soliton solutions of the M-fractional Kairat-II equation. Initially, soliton solutions are obtained using the new extended direct algebraic method. To enhance understanding, 2D and 3D graphical visualisations are presented, offering insights into the evolution and interactions of soliton structures. Subsequently, a Galilean transformation is applied to convert the model into an ordinary differential system, enabling the study of its sensitivity and dynamical properties. Finally, the chaotic nature of the model is explored using phase portraits, time series analysis, bifurcation diagrams, and Lyapunov exponents and Poincare maps. The findings have potential applications in physics, engineering, and signal processing, where understanding nonlinear wave propagation and chaotic systems is crucial.