Numerical analysis of some models for internal waves

In this talk the derivation and dynamics of some 1D models for the propagation of internal waves are reviewed. From the starting point of the corresponding Euler equations and under certain physical hypotheses, Boussinesq-type systems are derived. Then a numerical analysis of the models, based on the approximation with spectral methods and efficient time integrators, is developed. This will be finally used to study, by computational means, some issues of their dynamics, mainly focused on the solitary wave solutions.