Bäcklund transformations, rational solutions and soliton–cnoidal wave solutions of the modified Kadomtsev–Petviashvili equation. (March 2019) - Zhao, Zhonglong
Abstract: In this paper, the truncated Painlevé expansion is employed to derive the Bäcklund transformation and the n th Bäcklund transformation of the modified Kadomtsev–Petviashvili equation. The method for constructing the rational solutions with the aid of the Bäcklund 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.