The Hamilton Structure And Continuous Limit Of ASemi-discrete MKdV Equation

In this paper, we study the Hamilton structure and continuous limit of asemi-discrete mKdV equation and the Hamilton structure of a semi-discrete AKNSsystem. The main contents are summarized as follows:In chapter1, we outline the research background and motivation of this paper,mainly is the continuous limit theory of the semi-discrete integrable system.In chapter2, we study the continuous limit of a coupled semi-discrete mKdVequation.In chapter3, we study the Hamilton structure of a semi-discrete mKdV equation.In chapter4, we study the Hamilton structure of a semi-discrete AKNS equation.