a reduced model for internal waves interacting with submarine ...

in particular that of solitary waves. This is part of our future goals. The dynamics
described include wave scattering, dispersion and attenuation among other phenomena.
The work is organized as follows. In Chapter 2 the physical setting is presented
and as the main result, a reduced strongly nonlinear one-dimensional model is proposed.
Section 2.1 is devoted to obtaining a set of upper layer averaged equations
that will be completed with information provided by the lower layer in order to
derive the reduced model. The continuity of pressure at the interface establishes
a connection between both layers, as shown in Section 2.2. Through this condition
we add the topography information to the averaged upper layer system. The
case when the depth of the bottom layer approaches infinity is also considered. In
Section 2.3 the dispersion relations for the linearized models are computed. An
ILW equation with variable coefficient and the BO equation are obtained from
the reduced models as unidirectional wave propagation models in Section 2.4. In
Section 2.5 theoretical solitary wave solutions are presented for the ILW equation
and for the Regularized ILW equation. The purpose of Chapter 3 is to exhibit a
model that improves the order in the asymptotic approximation in the pressure
term of the reduced model obtained in Chapter 2. To that end, in Section 3.1
one more term of the asymptotic expansion of the mean horizontal derivative of
pressure is added to the upper layer averaged equations. Then, in Section 3.2, the
approximation of the pressure at the interface is improved and a reduced strongly
nonlinear one-dimensional model of higher-order is obtained. The dispersion relations
for the higher-order model and for the previous model are compared with
the full dispersion relation originating from the Euler equations in Section 3.3.
Chapter 4 is devoted to the numerical resolution of the reduced model obtained
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