On a nonlocal Boussinesq system for internal wave propagation

In this paper we are concerned with a nonlocal system to model the propagation of internal waves in a two-layer interface problem with rigid lid assumption and under a Boussinesq regime for both fluids. The main goal is to investigate aspects of well-posedness of the Cauchy problem for the deviation of the interface and the velocity, as well as the existence of solitary wave solutions and some of their properties.