The (2+1)-D generalized B-type Kadomtsev–Petviashvili (BKP) equation is studied in this work utilizing Painlevé property, Lie-symmetry method and generalized Kudryashov method (GKM). This study aims to pass the Painlevé test and obtain variant exact solutions for the (2+1)-D BKP equation that occurs in physical dynamics. First, we demonstrated that the governing equation exceeds the Painlevé test by using the Painlevé property. Symmetry analysis is utilized to obtain infinitesimals and vector fields of the BKP equation. The governing equation was converted to several ordinary differential equations (ODEs) using linear combinations of these vectors. GKM is used to generate a novel class of closed-form solutions for the BKP equation. Many random constants and functions were included in the derived solutions to improve their dynamic characteristics. The emergence of solutions was facilitated by the optimal selection of estimates for these elective constants. There are several types of solution behavior, such as a kink wave, solitary wave, anti-kink wave, and single wave.
Gaber et al. (Mon,) studied this question.