Stability of Forced Steady Solitary Waves

This paper explores the basic mechanism underlying the remarkable phenomenon that a forcing excitation stationary in character and sustained at near resonance in a shallow channel of uniform water depth generates a non-stationary response in the form of a sequential upstream emission of solitary waves. Adopting the forced Korteweg-de Vries (fKdV) model and using two of its steady forced solitary wave solutions as primary flows, the stability of these two transcritical steady motions is investigated, and their bifurcation diagrams relating these solutions to other stationary solutions determined, with the forcing held fixed. The corresponding forcing functions are characterized by a velocity parameter for one, and an amplitude parameter for the other of the steadily moving excitations