New Modified Jacobi Elliptic Function Expansion Method and Its Application to (3+1)-Dimensional KP Equation

With the aid of computerized symbolic computation, the new modified Jacobi elliptic function expansion method forconstructing exact periodic solutions of nonlinear mathematical physics equation is presented by a new general ansatz. The proposed method is more powerful than most of the existingmethods. By use of the method, we not only can successfully recover the previously known formal solutions but also can construct new and more general formal solutions for some nonlinear evolution equations. We choose the (3+1)-dimensionalKadomtsev-Petviashvili equation to illustrate our method. As aresult, twenty families of periodic solutions are obtained. Ofcourse, more solitary wave solutions, shock wave solutions ortriangular function formal solutions can be obtained at their limitcondition.