The Backlund Transformation And Exact Solutions Of Boussinesq-Burgers And Benjamin-One Equations

In the soliton theory,according to the link between a complex equation with a simple equation to obtain the solution of complex equation is an effective means of solving. Backlund transformation is the relationship between the solutions,so it has special significance for solving partial differential equations. With the help of symbolic computation software Maple,this paper mainly studied the theory of C-D pairs,WTC test and the extended homogeneous balance method and their application in seeking Backlund transformation. Specified As follows:Introduction, we mainly introduces the development process of the soliton, background and research method of the Backlund transformation and gives a brief introduction of the link between the curvilinear motion and soliton equations.Capter1states the theory of C-D pairs, including basic thought and its application in seeking Backlund transformation.Capter2introduces the soliton equations derived by the pseudospherical movement, and the process of construction Backlund transformation to these equations.Capter3Accoding to the Kruskal simplified method, WTC truncated expansion method, the Painleve integrability condition and the Backlund transformation of a variable-coefficient equation are abtained.Capter4Making use of the extended homogeneous balance method, several groups Backlund transformation and the abundant exact solutions of the Boussinesq-Burgers equation and Bnejamin-One equation are obtained. Further obtained the similarity reduction and solution of the Boussinesq-Burgers equation.