Symmetry reductions and new exact non-traveling wave solutions of potential Kadomtsev–Petviashvili equation with p-power

With the aid of Maple symbolic computation and Lie group method, PKPp equation is reduced to some (1+1)-dimensional partial differential equations, in which there are linear PDE with constant coefficients, nonlinear PDE with constant coefficients, and nonlinear PDE with variable coefficients. Using the separation of variables, homoclinic test technique and auxiliary equation methods, we obtain new abundant exact non-traveling solutions with arbitrary functions for the PKPp.