The classical Korteweg-de Vries equation (KdV for short) and its alternative, the regularized long-wave equation (RLW), also called the Benjamin, Bona, Mahony (BBM) equation, are mathematical models that approximately describe surface waves in shallow water in certain regimes. Both the KdV and BBM equations are globally well-posed in a wide range of Sobolev spaces and possess solitary-wave solutions. Furthermore, solitary-wave solutions are all stable.
Systems of coupled KdV equations and coupled BBM equations appear in various applications. There is far less known about them and it appears that their theory is considerably more complicated. The focus of the discussion in the seminar is existence, stability and instability of solitary-wave solutions for systems of these sorts.