Interaction of internal solitary waves with long periodic waves within the rotation modified Benjamin–Ono equation

The interaction of a solitary wave with a long background periodic wave in a deep ocean is studied within the framework of the rotation modified Benjamin–Ono equation. Using a multiple scales analysis, we find stationary and nonstationary solutions for a Benjamin–Ono soliton trapped within a long sinusoidal wave. We show that the radiation losses experienced by the soliton and caused by the Earth’s rotation can be compensated by energy pumping from the background wave. However, the feedback of the soliton on the background wave eventually leads to the destruction of the coherent structure and energy dispersion in a quasi-random wave field. Estimates of the characteristic parameters of the soliton dynamics are presented for real oceanic conditions. •The interaction of Benjamin–Ono solitary waves with a long background periodic wave is studied.•Stationary and nonstationary regimes of trapped solitons are found.•Estimates of the characteristic parameters of the solitons are presented for real oceanic conditions.