Two main research areas are considered:
The first one is the exact theory of the existence and stability of surface waves on water of finite depth. Using the exact nonlinear governing equations of the fluid motion, we can prove the existence of various two-dimensional or three-dimensional nonlinear surface waves and obtain the linear and nonlinear stability of these waves.
The second research area is the study of the well-posedness for the initial boundary value problems of some nonlinear model equations arising from water-wave problems, such as Kortweg-de Vries equation, nonlinear Schrodinger equations, Benjamin-Bona-Mahony equation, Kadomtsev-Petviashvili equation, etc. Moreover, we can prove the existence of solitary-wave solutions for these model equations and show the orbital stability of these solutions.