Symbolic-computation study of integrable properties for the (2 + 1)-dimensional Gardner equation with the two-singular manifold method

Abstract

The singular manifold method from the Painleve analysis can be used to investigate many important integrable properties for the non-linear partial differential equations. In this paper, the two-singular manifold method is applied to the (2 + 1)-dimensional Gardner equation with two Painleve expansion branches to determine the Hirota bilinear form, Backlund transformation, Lax pairs and Darboux transformation. Based on the obtained Lax pairs, the binary Darboux transformation is constructed and the N × N Grammian solution is also derived by performing the iterative algorithm N times with symbolic computation.