Some Properties For Deep-water Solitary Waves

The mathematical problem of water waves is always one of the hot topics in the study of mathematical hydromechanics,which includes the study of the motion state and properties of solitary waves.In this paper,the velocity field,pressure field and the trajectories of particles for deep-water waves are studied in detail by using the strong maximum principle,weak maximum principle and the Dubreil-Jacotin transformation.The structure of the paper is as follows:Chapter 1 introduces the origin,research background and research status of solitary wave at home and abroad.Chapter 2 introduces some preliminary knowledge,including strong maximum principle,weak maximum principle and Hopf maximum principle,before giving the main results of this paper.In chapter 3,some properties of the velocity and pressure field of irrotational deep-water solitary waves are studied,and the trajectories of particles is discussed.In this paper,we first introduce the stream function and the governing equations in the moving frame of the irrota-tional deep-water solitary waves,and then discuss the velocity and pressure properties of the solitary waves by means of the hodograph transformation and maximum principle,and give the trajectories of particles according to the motion characteristics of the water waves.In chapter 4,we study the properties of the velocity and pressure fields of the deep-water solitary waves with vorticity.Based on the Dubreil-Jacotin transformation and the maximum principle,we prove some properties of the horizontal and vertical velocities on the streamline of deep-water solitary waves with vorticity in a moving frame.At the same time,we also prove R?0(R=1/2|??|2+gy-1/2Q-?(?)),while the curl ? meets certain conditions.