HYSTERESIS PHENOMENA IN THE INTERACTION OF A DAMPED SOLITARY WAVE WITH AN EXTERNAL FORCE

The problem of the interaction of a damped solitary wave with a moving external isolated force within a forced dissipative Korteweg-de Vries equation is studied. An analytical model for this interaction is pres ented based on a small amplitude for the external force. It is shown t hat capture of the solitary wave by the external force is possible for either sign of the force. Hysteresis effects occur for slow variation s of the speed of the external force. Numerical simulation of the forc ed Korteweg-de Vries equation with dissipation confirm the conclusions of the analytical theory.