Instability Of Ground States For A Generalized Davey-Stewartson System

The Davey-Stewartson system is a mathematical model which describes free surface waves subject to the effects for both gravity and capillarity.We mainly study the instability of standing waves of the Davey-Stewartson system,and prove the strong instability of standing waves under some conditions.This thesis is divided into three chapters.The first chapter is an introduction,which introduces the physical background of the Davey-Stewartson system and the related research results.The second chapter is the preliminaries,which introduces the local well-posedness of the Davey-Stewartson system and the variational characteristics of ground state solutions.Chapter 3 is the proof of the main conclusion.