Wronskian rational solutions to the generalized (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation in fluid dynamics

The main topic of the paper is to investigate the generalized (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) and Korteweg-de Vries (KdV) equations, which are widely used in many physical areas, especially in fluids. A new Wronskian formulation is presented for these two equations associated with the bilinear Backlund transformation. Based on Wronskian identities of the bilinear Kadomtsev-Petviashvili (KP) hierarchy, the Wronskian determinant solution is verified by a direct and concise calculation. The newly introduced Wronskian formulation provides a comprehensive way for building rational solutions. A few rational Wronskian solutions of lower order are computed for the generalized (2 + 1)-dimensional DJKM equation. Our work can show that the extended (2 + 1)-dimensional KdV equation possesses the similar rational Wronskian solutions through the corresponding logarithmic transformation.