The Exact Solutions Of 2D Toda Lattice Equation

In this paper,based on the mathematical mechanization and AC=BDmodel,bilinear 2D Toda lattice differential-difference equation is studied in detail.Condition of solution existence for 2D Toda lattice differential-difference equation in the lower dimension is analyzed and simplified,and we also apply the theory of AC=BD to seek the analytic solution in two-dimensional case.The arrangement of this paper is as follows with four parts.In Chapter 1,the history and present situation of mathematical mechanization are mainly introduced initially.We also summarize the basic ideas,development situation and application of the theory of AC=BD here.In addition,we present the characteristics of differential-difference equation and introduce the Toda lattice equation emphatically.In Chapter 2,we mainly introduce the theory of AC=BD and its application in seeking the solution of differential equation.In Chapter 3,we mainly introduce the deduction of bilinear 2D Toda lattice equation and its existence conditions of solution.Also,we give the its form of analytical solution and analyze the results.In Chapter 4,we analyze the existence conditions of analytical solution for 2D Toda lattice equation in Chapter 3.And we simplify the condition of solution and give the method of seeking the solution in the lower dimensional situation.And we apply the theory of AC=BD to seek the analytical solution for bilinear 2D Toda lattice equation.Finally,we summarize our work and point out the development prospect in seeking the solution of bilinear 2D Toda lattice equation.