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

The singular manifold method from the Painlevé 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 Painlevé expansion branches to determine the Hirota bilinear form, Bäcklund transformation, Lax pairs and Darboux transformation. Based on the obtained Lax pairs, …