The Date–Jimbo–Kashiwara–Miwa equation describes the wave diffusion of a physical quantity and plays a central role in modeling nonlinear wave propagation in higher‑dimensional integrable systems. It has important applications in plasma physics, fluid mechanics and nonlinear wave theory, where it governs the dynamics of soliton structures, coherent wave packets and other collective excitations. In this study, we investigate the (2+1)‑dimensional Date–Jimbo–Kashiwara–Miwa equation, which governs important classes of integrable nonlinear waves in (2+1) dimensions. Using an extended modified auxiliary equation mapping technique, we construct a wide variety of exact traveling wave solutions. These include solitary‑wave solutions, kink‑type (or shock‑type) waves, periodic wave patterns and rational solutions, all expressed in terms of suitable auxiliary‑equation basis functions. The resulting solutions provide new explicit forms that enrich the known solution space of the Date–Jimbo–Kashiwara–Miwa equation and generalize or complement previously reported results. To highlight the physical structure and spatial behavior of these solutions, we include corresponding 3D plots that clearly illustrate their wave profiles, amplitude modulation, and localization properties. The combination of analytical construction and graphical visualization demonstrates the effectiveness of the approach in capturing rich wave structures in higher‑dimensional integrable equations and contributes to a deeper understanding of exact nonlinear wave propagation in (2+1)-dimensional physical systems.