Three-fluid system short-wave instability and gap-solitons

Abstract

The short-wave instability arising due to the resonace between two wave modes for a three-fluid system of a stratified and sheer flow is addressed. A weakly nonlinear analysis leads to a class of solitary waves, widely known as gap-solitons in other physical contexts. The essential ingredients are the existence of a spectral gap between two branches of the dispersion relation, and the development of a set of envelope equations to describe weakly nonlinear waves, whose carrier frequency and wavenumber belong to the centre of this gap. For the special case where the gap-soliton is a steady travelling wave of the full fluid system, we show that there is large class of such gap-solitons.