The Application Of AC=BD Theory To Solving Differential Equations Mechanically

In this dissertation, by applying the ideas of the mathematics mechanization, under the instruction of " AC=BD" theory of Professor Zhang Hongqing, we consider some methods seeking exact solutions to 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 methods for constructing solutions to the nonlinear partial differential equation(s). In addition, some domestic achievements and foreign ones on the subject are presented.Chapter 2 concerns the construction of exact solutions to nonlinear partial differential equation(s) under the uniform frame work of "AC=BD" theory. The basic theory and application regarding "AC=BD" model and the construction of operators C and D are introduced.Chapter 3 introduces an algebraic method for finding exact solutions to nonlinear evolution equations. An improved algebraic method is provided and several nonlinear evolution equation are taken to illustrate the application of the improved method. The improved method can be used to obtain more formal exact solutions to nonlinear partial differential equations.