Lie Symmetry Analysis and Conservation Laws for the (2 + 1)-Dimensional Dispersionless B-Type Kadomtsev–Petviashvili Equation

Abstract

The Lie symmetry analysis is adopted to the (2 + 1)-dimensional dispersionless B-type Kadomtsev–Petviashvili (dBKP) equation. The combination of symmetry analysis and symbolic computing methods proves that Lie algebra of infinitesimal symmetry of the dBKP equation depends on four independent arbitrary functions and one arbitrary parameter. The Lie algebra is reduced to four classes for deriving commutative relations, group invariant solutions of dBKP equation and conservation laws, and the optimal system of 1-dimensional subalgebras from one class is constructed. Based on the optimal system and other particular infinitesimal symmetries, plentiful symmetry reductions and invariant solutions are computed by using Lie group method. Six successive symmetries and conserved quantities of the dBKP equation are linked by the new conservation theorem. Besides, exact solution of the dBKP equation is constructed according to a conservation vector.