The AC=BD Model And Its Application To The Exact Solutions Of Partial Differential Equation

In this dissertation, by applying the ideas of the mathematics mechanization, under the instruction of the "AC=BD" theory of Professor Zhang Hongqing,we consider some methods seeking exact solutions for the nonlinear partial differential equation(s) arising from the fields of elasticity,fluid mechanics, aerodynamics, plasma physics, biophysics and chemical physics.Chapter 1 of this dissertation is devoted to investigating the theory and application of mathematics mechanization; reviewing the history and development of the soliton theory and the construction of the nonlinear partial differential equation. In addition, some domestic achievements and abroad ones on the subject are presented.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.Chapter 3 constructs the general solution of the clastic equations which could be programmed by the symbolic language-Maple.Chapter 4 is devoted mainly to the generalized projective Riccati equations method.The generalized method is shown to solve some typical nonlinear evolution cquations.We get abundant exact solutions(including solitary solutions, soliton-like solutions, periodic solutions, periodic-like solutions and rational solutions etc.)of them by using the method.