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.