Forced Benjamin-Ono equation and its application to soliton dynamics.

Abstract

The propagation of long interfacial waves of finite amplitude is investigated in a two-layer fluid system where a layer of a light fluid overlies a layer of heavier fluid resting on an uneven bottom. The upstream condition is imposed such that the constant flow is in the same direction in both layers. Under the appropriate balance among nonlinearity, disperison, and topographic effect, the long-term evolution of the interfacial elevation is shown to be governed by a forced Benjamin-Ono (fBO) equation. A direct soliton perturbation theory is applied to the fBO equation to study the interaction of an algebraic soliton with a bottom topography when the Froude number is nearly equal to unity. A system of ordinary differential equations describing the change of the amplitude and position of the soliton is derived for a simple bottom profile. The solutions of these equations exhibit a variety of phenomena, such as the capture and repulsion of the soliton by topography and the occurrence of solitonlike phase shifts due to the interaction of the soliton with topography. We also examine the effect of small dissipation on the dynamics of the soliton. Special emphasis is given to the appearance of a branch of stationary states of the soliton which has not previously been observed in the absence of dissipation. (c) 1995 The American Physical Society