New mathematical model governing the propagation of two-wave modes moving in the same direction: Classical and fractional potential KDV equation

Abstract

Abstract. In this study, we devote our effort in investigating the behavior of a new two-mode potential Korteweg-de Vries (KdV) equation. This model describes the motion of two waves propagating in the same direction simultaneously. The interaction of the so-called two-wave modes depends on the increasing of embedded phase velocity. Three robust schemes are utilized to find explicit solutions to this new model. Moreover, the time-space fractional version of the two-mode potential KdV equation is investigated. Finally, a graphical analysis is provided to study some physical aspects of these traveling waves.