On the controllability of a model system for long waves in nonlinear dispersive media

Considered here is a higher-order generalization of the classical Boussinesq system which models the two-way propagation of small-amplitude, long wavelength, gravity waves on the surface of water in a canal or the propagation of long-crested waves on large lakes and oceans. Our aim is to investigate the controllability properties of this nonlinear model in terms of the values of the parameters involved in the system. We give general conditions which ensure both the well-posedness and the local exact controllability of the nonlinear problem in some well chosen Sobolev spaces.