Coupled system of Korteweg–de Vries equations type in domains with moving boundaries

We consider the initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for the coupled system of equations of Korteweg–de Vries (KdV)-type modelling strong interactions between internal solitary waves. Finite domains of wave propagation changing in time arise naturally in certain practical situations when the equations are used as a model for waves and a numerical scheme is needed. We prove a global existence and uniqueness for strong solutions for the coupled system of equations of KdV-type as well as the exponential decay of small solutions in asymptotically cylindrical domains. Finally, we present a numerical scheme based on semi-implicit finite differences and we give some examples to show the numerical effect of the moving boundaries for this kind of systems.