Terminal damping of a solitary wave due to radiation in rotational systems

The evolution of a solitary wave under the action of rotation is considered 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 with 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 wave disappears in a finite time. The radiated wave amplitude and the structure of the radiated "tail" in space-time are also found. Some numerical results, which confirm the approximate theory developed here, are given.