Symmetry Reductions and Explicit Solutions of (3 + 1)-Dimensional Kadomtsev-Petviashvili (KP) Equation

Abstract

With the aid of symbolic computation, we use the Lie group method to find the Lie point symmetries of (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation, and reduce the equation with the obtained symmetries. As a result, many kinds of new symmetry reductions have been presented, including the (2+1)-dimensional KP type equation. And some explicit solutions are given due to the Riccati equation meth