Ac = Bd And Its Nonlinear Equations In Applications

The major contents in this paper include:with the aid of many types of constructive transformations and symbolic computation, some topics in nonlinear waves and integrable system are studied, including exact solutions,Liouville integrable hie-rarchy,and its N-Hamilton structure, constraint flow, Lax representation, r-matrix,in-volutive system and involutive solutions.Chapter 2 is devoted to investigating exact solutions of nonlinear wave equations: Firstly, the basic theories of C-D pair and C-D integrable system are presented. Secondly, we choose some examples to illustrate them .Based on Prof. Zhang hong-qing' AC=BD theory, using one of Dr.Yan zhenya' transformations based on one Riccati equation, twenty-six families of exact solutions of Modified Improved Bou-sinnesq equation are found, including new solitary solution and periodic solution, except solutions given by literature[65].Chapter 3 concentrates on new Lax integrable hierarchies of equations and Liouville integrable N-Hamilton structures. A spectral problem is studied by using the Tu's scheme , its Lax integrable hierarchies of equations and Liouville integrable Hamilton structures are obtained , r-matrix, new involutive system and involutive solutions of Bargman constraint flow of this hierarchy are found.In chapter 4,Maxwell equations presented in the form of exterior and codiff-erential are studied , and Maxwell equations and charge conservation law can be derived by each other. In particular , the derivation of Maxwell equations from charge conservation law is very important for the discovery of unknown physical law.