Ac = Bd In The Backlund Transformation And Partial Differential Equations Of Completeness,

In this dissertation, by applying the ideas of the mathematics mechanization, under the instruction of the AC=BD model of Professor Zhang Hongqing, the nonlinear partial differential algebraic equation or equations (PDAE or PDAEs) related to some nonlinear topics which origin from physics, mechanics et al are studied, including exact solutions, Backlund transformation, the compatibility of the solutions and so on.Chapter 1 is devoted to investigating the idea, application, history and development of the mathematics mechanization and the construction of the solutions of nonlinear partial differential equation(NPDE). In addition, some achievements on the subject domestic and abroad are presented.Chapter 2 considers the construction of exact solutions of NPDE(s) under the instruction of the AC=BD model. The basic concept and theory about AC=BD model, the construction of the operators of C and D, the theory of C-D integral system are introduced. In addition, this dissertation introduces the methods of transforming NPDE into standard type advanced by Reid.Chapter 3 applies AC=BD model to Backlund transformation by the ideas of the mathematics mechanization. The basic concepts of the explicit and implicit C-D pair, Backlund transformation are presented. The arithmetics and examples are also presented.Chapter 4 introduces Wu differential character set, division with remainder and the compatibility of the solutions (local) of linear PDEs.