Bäcklund transformations and solutions of a generalized Kadomtsev - Petviashvili equation

In this paper, the bilinear form of a generalized Kadomtsev - Petviashvili equation is obtained by applying the binary Bell polynomials. The N-soliton solution and one periodic wave solution are presented by use of the Hirota direct method and the Riemann theta function, respectively. And then the asymptotic analysis demonstrates one periodic wave solution can be reduced to one soliton solution. In the end, the bilinear Bäcklund transformations are derived.