Transformation groups, Kac-Moody-Virasoro algebras and conservation laws of the Bogoyavlenskii-Kadomtsev-Petviashvili equation

In this paper, by using the generalized symmetry method we get the symmetries, Kac-Moody-Virasoro (KMV) type Lie algebras of the Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation. Based on the obtained symmetry structure, we directly construct the generalized transformation groups for the BKP equation. It can be divided into two types of subgroups, one is the Lie symmetry group and the other is the discrete symmetry group. Finally, we also give the conservation laws by using Ibragimov's theorem.