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.

We study the temporal equation of radiating stars by using three powerful methods for the analysis of nonlinear differential equations. Specifically, we investigate the global dynamics for the given master ordinary differential equation to understand the evolution of solutions for various initial conditions as also to investigate the existence of asymptotic solutions. Moreover, with the application of Lie’s theory, we can reduce the order of the master differential equation, while an exact similarity solution is determined. Finally, the master equation possesses the Painlev\’{e} property, which means that the analytic solution can be expressed in terms of a Laurent expansion.