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

TL;DR

This paper investigates how internal solitary waves interact with long background waves within the rotation modified Benjamin-Ono equation, revealing energy exchange mechanisms and the conditions for wave stability or destruction.

Contribution

It introduces asymptotic solutions for soliton trapping within long waves and analyzes the effects of Earth's rotation on wave energy dynamics.

Findings

Solitons can be trapped within long waves under certain conditions.

Earth rotation causes radiation losses that can be balanced by background energy.

Soliton influence can lead to wave structure destruction and energy dispersion.

Abstract

Interaction of a solitary wave with a long background wave is studied within the framework of rotation modified Benjamin-Ono equation describing internal waves in a deep fluid. With the help of asymptotic method, 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 a soliton and caused by the Earth rotation can be compensated by the energy pumping from the background wave. However, the back influence 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.