Recurrent solutions of the Schrödinger-KdV system with boundary forces

In this paper, we consider the Schrodinger-KdV system with time-dependent boundary external forces. We give conditions on the external forces sufficient for the unique existence of small solutions bounded for all time. Then, we investigate the existence of bounded solution, periodic solution, quasi-periodic solution and almost periodic solution for the Schrodinger-KdV system. The main difficulty is the nonlinear terms in the equations, in order to overcome this difficulty, we establish some properties for the semigroup associated with linear operator which is a crucial tool.