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Different nonlinear dust-ion-acoustic waves are studied in a plasma composed of isothermal electrons, warm positive ions, and stationary negatively charged dust particles. For this purpose, Kadomtsev–Petviashivili (KP) equation is derived using the reductive perturbation technique. An extended homogeneous balance method is used to obtain different solutions of KP equation describing a wide variety of nonlinear waves. The present results are of interest to understand the localized waves that may occur in laboratory or in space dusty plasmas such as Saturn’s rings.