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

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.

Automated summary

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 and optimal system are obtained through Lie symmetry analysis. The reduced partial differential equations are transformed into ordinary differential equations using traveling wave transform, and the exact solutions are found using the extended tanh-function method. The structural features of exact solutions at different times are illustrated with images.