Non-auto Bäclund transformation, nonlocal symmetry and CRE solvability for the Bogoyavlenskii–Kadomtsev–Petviashvili equation

In this paper, we study the Bogoyavlenskii–Kadomtsev– Petviashvili (BKP) equation by using the truncated Painlevé method and consistent Riccati expansion (CRE). Through the truncated Painlevé method, its nonlocal symmetry and non-auto Bäcklund transformation are presented. The nonlocal symmetry is localized to a local Lie point group via a prolonged system. Moreover, with the help of the CRE method, we prove that the BKP equation is CRE solvable. Finally, the kink-lump wave interaction solution of BKP equation is explicitly given by using the trilinear form. The interaction between kink wave and lump wave is investigated and exhibited mathematically and graphically.