Abstract
This article deals with the (3+1)-dimensional variable coefficient Date–Jimbo–Kashiwara–Miwa equation which describes the behavior of waves as they travel through nonlinear dispersive media. The integrability of this equation has been evaluated by mean of Painlevé property. An auto-Bäcklund transformation of the considered equation is being produced with the aid of Painlevé analysis. To get the analytic solutions of the considered equation, the auto-Bäcklund transformation method is employed. Three new analytical solution families including complex solution have been derived successfully via the auto-Bäcklund transformation method. All the results have been plotted in three-dimension by taking different parameter values and functions. These solutions depict the kink-antikink wave, periodic wave, complex periodic wave and complex kink-antikink wave solutions for the considered equation.
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