Lax pair, binary darboux transformation and new grammian solutions of nonisospectral kadomtsevpetviashvili equation with the two-singular-manifold method

Abstract

In this letter, the two-singular-manifold method is applied to the (2+1)-dimensional nonisospectral KadomtsevPetviashvili equation with two Painlevé expansion branches to determine auto-Bäcklund transformation, Lax pairs and Darboux transformation. Based on the two obtained Lax pairs, the binary Darboux transformation is constructed and then the Nth iterated transformation formula in the form of Grammian is also presented. By using these Darboux transformations, we obtain some new grammian solutions. © 2010 2010 The Author(s).