LAUSR

Abstract In this paper, the Mth-order lump solutions for the (2+1)-dimensional Kadomtsev–Petviashvili I equation are studied. Firstly, the Nth-order wronskian determinant solutions of the Hirota bilinear form of the (2+1)-dimensional Kadomtsev–Petviashvili I equation are given. Then, the 1st-order lump solution is obtained by making elementary transformations and taking limit to the 2nd-order wronskian determinant solution. Next, the 2nd-order lump and the 3rd-order lump solutions are also similarly derived. The dynamic properties and characteristics of these low-order lump solutions are presented by three-dimensional images and the corresponding contour plots. Finally, based on the character of Vandermond determinant, the determinant expression of the Mth-order lump solutions is constructed by making elementary transformations and taking limit to the 2Mth-order wronskian determinant solutions.