A new (n+1)-dimensional generalized Kadomtsev-Petviashvili equation: Integrability characteristics and localized solutions

Abstract In this paper, an integrable generalization of the Kadomtsev-Petviashvili (KP) equation in arbitrary spatial dimension is proposed. Firstly, the singularity manifold analysis is performed to prove that the (n+1)-dimensional KP equation with general form is Painleve integrable. Secondly, combining the truncated Painleve expansion and binary Bell polynomial approach, the integrable characteristics of the (n+1)-dimensional KP equation are derived systematically, including N-soliton solution, bilinear Backlund transformation, the associated Lax pair as well as infinite conservation laws. Moreover, various types of localized solutions can be constructed starting from the N-soliton solutions. The abundant interactions including overtaking solitons, head-on solitons, one-order lump, two-order lump, breather, breather-soliton mixed solutions are analyzed by some graphs.