TERMINAL DAMPING OF A SOLITARY WAVE DUE TO RADIATION IN ROTATIONAL SYSTEMS

The evolution of a solitary wave under the action of rotation is consi dered within the framework of the rotation-modified Korteweg-de Vries equation, Using an asymptotic procedure, the solitary wave is shown to be damped due to radiation of a dispersive wave train propagating wit h the same phase velocity as the solitary wave. Such a synchronism is possible because of the presence of rotational dispersion. The law of damping is found to be ''terminal'' in the sense that the solitary wav e disappears in a finite time. The radiated wave amplitude and the str ucture of the radiated ''tail'' in space-time are also found. Some num erical results, which confirm the approximate theory developed here, a re given.