Homotopy perturbation method for higher dimensional nonlinear evolutionary equations

In this paper, an iterative numerical solution of the higher-dimensional (3+1) physically important nonlinear evolutionary equations is studied by using the homotopy perturbation method (HPM). For this purpose, the Kadomstev-Petviashvili (KP) and the Jumbo-Miwa (JM) equations are analyzed with the HPM and the available exact solutions obtained by the homogenous balance method will be compared to show the accuracy of the proposed numerical algorithm. The results approves the effectiveness and accuracy of the HPM.