The evolution of nonlinear wave packets in variable-coefficient Ostrovsky equation

Abstract

In this work, the effect of variable medium is taken into account to the Ostrovsky equation, namely variable-coefficient Ostrovsky equation. Ostrovsky equation originally is obtained from Korteweg-de Vries equation with an additional linear non-local term representing the effects of background rotation. The addition of this term has the drastic effect of destroying the solitary wave solution. Instead an initial solitary-like disturbance decays into radiating oscillatory waves and eventually form a nonlinear wave packet. However, a uniform background state, it not sufficient to describe internal solitary waves in the ocean. So, the effect of variable medium on the propagation of oceanic internal solitary waves in the present of background rotation is studied. This effect alone to the Ostrovsky equation can change the size of amplitude and wave packet envelope.