Optimal System, Invariant Solutions and Conservation Laws of the
Dispersionless B type Kadomtsev-Petviashvili Equation
Abstract
In this paper, we consider the dispersionless B type
Kadomtsev-Petviashvili (dBKP) equation through quasi classical limit of
BKP equation. We investigate the existence of one-parameter point
transformations in which the dBKP equation remains invariant by
admitting a five-dimensional Lie algebra. For the admitted Lie
symmetries, we calculate the one-dimensional optimal system, a necessary
analysis to perform the reduction process. Using this, we obtain various
closed-form similarity solutions for the dBKP equation. In addition to
this, we also derive the associated conservation laws of this equation
through Ibragimov’s method.