AC=BD Theory And Solving Nonlinear Evolution Equations

In this dissertation, under the guidance of mathematics mechanization and the instructionof the AC=BD theory put forward by Prof. Zhang Hongqing, by means of symbolic computationsoftware, some problems in the theory of soliton are discussed. This thesis also introduces somemethods of seeking exact solutions for the nonlinear evolution equations arising from the fieldsof fluid mechanics, aerodynamics, plasma physics, biophysics and chemical physics.Chapter 1 is devoted to investigating the ideas of the mathematics mechanization andcomputer algebra, the history and development of soliton theory. In addition, some domesticachievements and foreign ones on the subject are presented.Chapter 2 investigates AC=BD theory and its application, and the methods of constructingof the operators of C and D are introduced.Chapter 3 introduces some methods of seeking exact solutions for nonlinear evolution equa-tions, such as B(?)cklund transformation, Darboux transformation, inverse scattering method,Painlevéanalysis method, AC=BD model, and so on. By presenting a more general anas(?)tz,we extended rational expansion method-Riccati equation rational expansion.