Inverse Scattering Transform for the Fifth-Order Fractional KdV Equation with a Self-Consistent Source

Source abstract

In this paper, we constract and integrate the fifth-order Riesz fractional KdV (fRfKdV) equation with a self-consistent source in the class of rapidly decreasing functions via the inverse scattering transform(IST) method. We show that fifth-order Riesz fractional KdV equation with self-consistent sources is alsoan important theoretical model, since it is a completely integrable system. For one soliton cases, explicit formulas for the solutions of the problem under consideration are derived as examples to simulate their spatial structures and analyze their structural properties by selecting different values of fractional orders. The results indicate that both the source and the fractional order significantly influence the velocity of soliton propagation, while no energy dissipation occurs through out the entire motion process. This behavior corresponds to a super-dispersive transport mechanism, which is an experimentally testable prediction of the present theory. Furthermore, the analysis reveals that the absolute value of wave velocity becomes larger as$\epsilon$ increases. This study contributes valuable insights into nonlinear dynamics and soliton behavior, improving the understanding of multifaceted wave interactions in nonlinear fractional equations.