Backlund Transformation And Exact Solutions For The (3+1)-Dimensional Constant-coefficient And Variable-coefficient KP Equations

In this thesis, our aim is mainly focused on applying Hirota bilinear method to (3+1)-dimensional Constant-coefficient and Variable-coefficient KP equations. Firstly, by introducing logarithm transfromation and rational transfromation, the Kadomtsev-Petviashvili(KP)equation is transformed into bilinear forms. Then, using exchange formulae we derive the Backlund trans-formation in bilinear forms for the (3+1)-dimensional KP equation. In section 3, solution to the KP equation is expressed by the Wronski-type determinant. In section 4, a pfaffian version of the (3+1)-dimensional KP equation is derived, Finally, a pfaffianized coupled equation is produced by using pfaffianization procedure and two forms pfaffian solution for the soliton equation were gived.