The Cauchy problem and stability of solitary waves for a 2D Boussinesq-KdV type system. (Q636963)

The author studies a system of partial differential equations describing evolution of 3D long water waves with small amplitude; this model can be reduced to a Boussinesq type system. This system can be further transformed into a 2D KdV-like system. Using this fact, the author establishes local-in-time existence of smooth solutions and further, for sufficiently small data, also global-in-time existence of a unique solution. Using a variational argument involving the characterization of the ground state solutions, he also shows the orbital stability of solitary waves.