Dynamical analysis and soliton solutions of the space–time fractional Kaup–Boussinesq system

Abstract

This research investigates the dynamics of the fractional Kaup–Boussinesq system. Dynamical tools, such as phase portraits, bifurcation diagrams, Poincaré maps, Lyapunov exponents, and sensitivity diagrams, are employed to illustrate the system’s response to initial conditions and variations in parameters. In order to uncover the non-linear complexities of the system, a periodic forcing term is introduced, and chaotic and quasi-periodic behavior is explored. Additionally, using the extended Jacobi elliptic function technique, novel solitary wave solutions are derived, emphasizing the impact of different parameters on non-linear wave behavior. Visual representations, such as density plots and 3D graphs, further enhance the understanding of the intricate dynamics of the system.