Backlund transformations, rational solutions and soliton-cnoidal wave solutions of the modified Kadomtsev-Petviashvili equation

In this paper, the truncated Painleve expansion is employed to derive the Backlund transformation and the nth Backlund transformation of the modified Kadomtsev-Petviashvili equation. The method for constructing the rational solutions with the aid of the Backlund transformation is presented. It is proved that the modified Kadomtsev-Petviashvili equation is CRE solvable. Then the soliton-cnoidal wave solutions are explicitly presented. These results are useful in explaining nonlinear wave phenomena in oceanography. (C) 2018 Elsevier Ltd. All rights reserved.