Similarity Reductions and Similarity Solutions of the (3+1)-Dimensional Kadomtsev--Petviashvili Equation

Employing the compatibility method, we obtain the symmetries of the (3+1)-dimensional Kadomtsev--Petviashvili (KP) equation. Four types of similarity reductions of the KP equation are obtained by solving the corresponding characteristic equations associated with symmetry equations. In addition, a lot of similarity solutions to the KP equation are obtained.