# American Institute of Mathematical Sciences

September  2021, 26(9): 5149-5170. doi: 10.3934/dcdsb.2020337

## Recurrent solutions of the Schrödinger-KdV system with boundary forces

 School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China

Received  May 2020 Published  September 2021 Early access  November 2020

Fund Project: This work is supported by NSFC Grant (11701078)

In this paper, we consider the Schrödinger-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 Schrödinger-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.

Citation: Mo Chen. Recurrent solutions of the Schrödinger-KdV system with boundary forces. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 5149-5170. doi: 10.3934/dcdsb.2020337
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