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

Searching for higher-dimensional integrable models is one of the most significant and challenging issues in nonlinear mathematical physics. This paper aims to extend classic lower-dimensional arbitrary spatial dimension. We investigate celebrated Kadomtsev–Petviashvili (KP) equation propose its (n+1)-dimensional extension. Based on singularity manifold analysis binary Bell polynomial method, it found that generalized KP has N-soliton solutions, also possesses Painlevé property, Lax pair, Bäcklund transformation as well infinite conservation laws, thus proven be completely integrable. Moreover, various types localized solutions can constructed starting from solutions. The abundant interactions including overtaking solitons, head-on one-order lump, two-order breather, breather-soliton mixed are analyzed by some graphs.