Studies On The Nonisospectral KP Equation

Various methods have been developed to search solutions for soliton equations. In these methods, Hirota bilinear method is very direct and simple, so it has aroused wildly attention and popularity among scholars. One part of this thesis is studying the nonisospectral KP equation. First, Gramm determinant solution to the nonisospectral KP equation is derived. Second, Backlund transformation for this equation is given. At last, coupled equations for this equation is given and two form pfaff solutions for the coupled equations are drived.Much attention has been paid to the problem of soliton equations with self-consistent sources these years. Recently, Hu Xingbiao and Wang Hongyan proposed an algebraic method to solve this kind of equations. The obvious virtue of this method is that the equation and its soliton solitions can be generated simultaneously. This new approach is called source generation proce-dure. The other part of this thesis is to construct soliton equations with self-consistent sources and find their soliton solutions via source generation procedure.