A numerical method to solve a nonlocal dispersive wave system

We use a spectral method to solve numerically a generalization of an integro-differential system proposed by Choi and Camassa [4] as a model to describe internal waves propagating at the interface of two immiscible inviscid fluids with different constant densities. The proposed numerical solver is able to capture well the dynamics of the solutions. The model is given in terms of the wave elevation and the fluid velocity U. Furthermore, we show that each component of a solitary-like solution (n,U) of the system satisfies approximately a generalized Intermediate Long Wave equation, provided that nonlinear and dispersive effects are small.