A family of Boussinesq systems was proposed by J. L. Bona, M. Chen and J.-C. Saut to describe the two-way propagation of small amplitude gravity waves on the surface of water in a canal. Our work considers a class of these Boussinesq systems which couples two Benjamin-Bona-Mahony type equations posed on a bounded interval. We study the stabilization of the resulting system when a localized damp...

An analytical solution of the Boussinesq equations for the motion of a viscous stably stratified fluid driven by a surface thermal forcing with large horizontal gradients (step changes) is obtained. This analytical solution is one of the few available for wall-bounded buoyancy-driven flows. The solution can be used to verify that computer codes for Boussinesq fluid system simulations are free o...

Based on the Nambu 3-bracket and operators of KP hierarchy, we propose generalized Lax equation triple. Under operator constraints, construct KdV hierarchy Boussinesq hierarchy. Moreover, present exact solutions some nonlinear evolution equations.