The (2+1)-dimensional potential Kadomtsev–Petviashvili equation: Its solitons and complexiton

In the present paper, the (2+1)-dimensional potential Kadomtsev–Petviashvili equation (2D-pKPE) that arises in the vast areas of applied sciences is explored. First, by employing particular transformations, the equivalent structures of the 2D-pKPE are constructed. Solitons and complexiton of the 2D-pKPE are then extracted using Hirota and exponential methods. In the end, Ma’s algorithm is formally employed to prove the Hirota N-soliton condition of the 2D-pKPE.