Wronskian And Pfaffian Skills Of Solving Soliton Equations

In this paper, the Hirota bilinear method is researched deeply. First, the definition and properties of bilinear differential operator is introduced. Then the steps of solving soliton e-quations are showed by solving the KDV equation. After that, the writer explains that how a soliton equation turns into a bilinear equation in detail. The next, many soliton equations with this method can be constructed. Superposition principle of bilinear equations are introduced and many examples are given. The (3+1) dimensional KP equation and (2+1) dimensional Boussinesq equation are solved with the Wronskian skills. The6th BKP equation is solved with the Pfaffian skills.