Analysis of the symmetry group and exact solutions of the dispersionless KP equation in n + 1 dimensions

The Lie algebra of the symmetry group of the (n + 1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili equation is obtained and identified as a semi-direct sum of a finite dimensional simple Lie algebra and an infinite dimensional nilpotent subalgebra. Group transformation properties of solutions under the subalgebra sl(2,R) are presented. Known explicit analytic solutions in the literature are shown to be actually group-invariant solutions corresponding to certain specific infinitesimal generators of the symmetry group.