Research Of The Method For Getting The Exact Solutions Of Partial Differential Equation(s) With The AC=BD Theory

In this dissertation, by applying the ideas of the mathematics mechanization introduced by Academician Wu Wenjun, under the instruction of the AC=BD theory put forward by Prof. Zhang Hongqing, with the aid of constructive transformation and symbolic computation, consider some methods seeking exact solutions for the nonlinear evolution equation(s) arising from the fields of fluid mechanics, aerodynamics, plasma physics, biophysics and chemical physics.Chapter 1 of this dissertation is devoted to investigating the ideas of mathematics mechanization and computer algebra;reviewing the history and development of the soliton theory and the construction of the nonlinear partial differential equation.Chapter 2 concerns the construction of exact solutions of nonlinear partial differential equation(s) under the uniform frame work of "AC=BD" theory. The basic theory and application about " AC=BD" model and the construction of the operators of C and D are introduced.In chapter 3,the tanh function method is improved and a new generalized Riccati equation rational expansion method which we have improved is presented. And then apply the methods to the H-S Equation, the compound KdV Equation and the (2+1)-Dimensional KdV-Burges Equation, respectively. Finally, we derive many new exact solutions: solitary solution, solitary-like solution, periodic solution, period-like solution, rational solution, and so on.