Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

Abstract

Based on the Hirota bilinear method, we systematically investigate the (3+1)-dimensional Boiti-Leon-Manana-Pempinelli (BLMP) equation in incompressible fluids and main results include: (1) the formulas of N-kink-soliton solutions and the bound states of multi solitons are all presented, (2) the lump solution is derived by the positive quadratic function method, (3) the interactional solutions are given, i.e., one lump interacts with one- and two-kink-soliton, (4) some special periodic solutions are discussed, i.e., lump-periodic solutions and homoclinic breather solutions.