A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions

Abstract In this article, the Date–Jimbo–Kashiwara–Miwa equation is extended to a new variable-coefficients equation with respect to the time variable. The infinitesimal generators are acquired by studying the Lie symmetry analysis of the equation, and the optimal system of this equation is presented. After that, the equation performed similarity reductions, and the reduced partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) with the help of traveling wave transform. Then, the exact solutions are found by applying the extended tanh-function method. Finally, the structural features of exact solutions to different times are shown with the help of images.