Gap-Solitons in a three-layer stratified shear flow
Date Issued
2007
Author(s)
Abstract
In this paper, we give an explicit asymptotic construction of a class of solitary waves,
widely known as gap-solitons in other physical contexts, for a certain three-layered fluid
flow. 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. Here we describe the gap-soliton solutions to this set of envelope equations. For
the special case of particular interest when the envelope and carrier speeds are identical,
so that the gap-soliton is a steady travelling wave of the full fluid system, we show that
there is large class of such gap-solitons.
widely known as gap-solitons in other physical contexts, for a certain three-layered fluid
flow. 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. Here we describe the gap-soliton solutions to this set of envelope equations. For
the special case of particular interest when the envelope and carrier speeds are identical,
so that the gap-soliton is a steady travelling wave of the full fluid system, we show that
there is large class of such gap-solitons.
Subjects
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