Nonlinear waves in rotating media

Dynamics of nonlinear waves in rotating media is considered. Particular attention is focused on surface and internal waves in a stratified ocean under the influence of the Earth's rotation and on magneto-acoustic waves propagating in magnetized rotating plasma. A model equation (Ostrovsky's equation) is derived from the basic set of equations taking into account Coriolis force. Stationary solutions of this equation are obtained numerically and by means of asymptotic method, and analyzed in detail. These include solitary-type solutions (solitons with monotonic and oscillating tails), complex multisolitons (bound states of coupled single solitons), as well as periodic waves. It is shown that positive dispersion (typical for plasma waves), in contrast to negative (typical for ocean waves), gives rise to specific solitary waves (Ostrovsky's solitons) having zero total "mass". Dynamics of KdV solitons in rotating systems is studied and compared with the dynamics of Ostrovsky's solitons. Results of laboratory modelling of internal wave dynamics in a rotating tank are presented. Decay laws of solitary waves due to cylindrical divergence in rotating media are studied. Dependencies of solitons amplitudes on distance both for KdV and Ostrovsky's solitons are obtained and compared. Different regimes of soliton decay are discovered and analyzed in detail. Some estimates for surface and internal waves in real oceanic conditions under the influence of the Earth's rotation are presented.