Constructing Nonlinear Travelling Wave Solutions Of Some Nonlinear Evolution Equations

In this dissertation, by applying the ideas of the mathematics mechanization introduced by Academician Wu wcnjun, 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 introducing the history and development of the soliton theory, the ideas of mathematics mechanization and computer algebra, and some methods seeking exact solutions for the nonlinear evolution equation, such as inverse scattering method, symmetry reduction method, Backlund transformation, Darboux transformation , Hirota bilinear method, Painleve analysis method, AC = BD model, and so on.Chapter 2 concerns the construction of exact solutions of nonlinear evolution 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 introduces the two methods- Extended F expansion method and generalized Riccati equation expansion which we have improved. And then apply the two methods to the (2+l)-Dimensional KdV Equation, the (2+l)-Dimensional breaking soliton Equation and (2+l)-Dimensional Broer -Kaup Equation, respectively. Finally, we derive many new exact solutions: solitary slution, solitary-like solution, periodic solution, period-like solution, rational solution, and so on.Chapter 4 is arranged as follows. At first, we introduce the theory of Painleve property and truncation expansion method. Then by means of Laurent scries truncation expansion method, derive the Backlund transformation of the (2+l)-Dimensional Nizhnik -Novikov -Veselov Equation. Finally, with the help of symbolic computation, we obtain abundant solutions of the (2+l)-Dimensional Nizhnik -Novikov -Veselov Equation.