The Explicit Solutions Of Two High-Dimensional Soliton Equations

In this dissertation,by applying the ideas of the mathematics mechanization introduced by Academican Wu wenjun,with the aid of symbolic computation software Maple,under the instruction of the AC=BD theory put forward by Professor Zhang Hongqing,considers some methods seeking exact solutions for the nonlinear partial diffcrcntial equations arising from the fields of fluid mechanics,aerodynamics,plasma physics,biophysics and chemical physics.Chapter 1 reviews the history and development of the soliton theory,the constrution of the nonlinear evolution equation(s),and several construtive methods based on bilinear method.In addition,the ideas of the mathematics mechanization and symbolic computation,some achieve-ments on the subject domestic and abroad are introduced.Chapter 2 is mainly devoted to AC=BD model and its applications in solving partial equation.The theory of AC=BD is applied to explain the essence of some well-known clas-sical methods solving soliton equations.And the construction of the operators of C and D is introduced.Chapter 3 firstly introduces Hirota bilinear method and Wronskian technique.Secondly, by introducing logarithmic transformation,N-soliton solution and its Wronskian form of(3+1)-dimensional YTSF equation are obtained with the aid of bilinear method.Finally,the new generalized multiple Riccati equations rational expansion method is presented,and we take (2+1)-dimensional breaking soliton equation for example to illustrate the effctiveness of the method.