Grammian solutions for a (2+1)-dimensional integrable coupled modified Date–Jimbo–Kashiwara–Miwa equation

In this paper, Grammian solutions to a (2[Formula: see text]+[Formula: see text]1)-dimensional modified Date–Jimbo–Kashiwara–Miwa (mDJKM) equation are presented by using Hirota bilinear method and perturbation expansion. Starting from the Grammian solutions, an integrable coupled mDJKM equation is then obtained and the corresponding Grammian solutions are first derived by utilizing the source generation procedure. Besides, we also construct and solve a coupled DJKM equation via source generation procedure. It is interesting that the coupled mDJKM system constitute a bilinear Bäcklund transformation for the coupled DJKM system. This means that the commutativity of source generation procedure and Bäcklund transformation is valid for the (2[Formula: see text]+[Formula: see text]1)-dimensional DJKM equation.