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

Abstract

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 Bäcklund 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.