Adjustment processes and radiating solitary waves in a regularized Ostrovsky equation

Abstract

The Ostrovsky equation is an adaptation of the Korteweg-de Vries equation widely used to describe the effect of rotation on surface and internal solitary waves. It has been shown that the effect of rotation is to destroy such solitary waves in finite time due to the emission of trailing radiation. Here this issue is re-examined for a regularized Ostrovsky equation. The regularization is necessary to remove an anomaly in the Ostrovsky equation whereby there is a discontinuity in the mass field at the initial moment. It is demonstrated that in the regularized Ostrovsky equation there is a rapid adjustment of the mass which is transported a large distance in the opposite direction to that in which the solitary wave propagates.