Reduced differential transform method for nonlinear integral member of Kadomtsev–Petviashvili hierarchy differential equations

Mohamed, Mohamed S.; Gepreel, Khaled A.

doi:10.1016/j.joems.2016.04.007

Reduced differential transform method for nonlinear integral member of Kadomtsev–Petviashvili hierarchy differential equations

Authors

Mohamed S. Mohamed ¹^{, 2}
Khaled A. Gepreel ³^{, 2}

¹ Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, Egypt

² Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia

³ Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

10.1016/j.joems.2016.04.007

Abstract

The main objective of this paper is to use the reduced differential to transform method (RDTM) for find- ing the analytical approximate solutions of two integral members of nonlinear Kadomtsev–Petviashvili (KP) hierarchy equations. Comparing the approximate solutions which obtained by RDTM with the exact solutions to show that the RDTM is quite accurate, reliable and can be applied for many other non- linear partial differential equations. The RDTM produces a solution with few and easy computation. This method is a simple and efficient method for solving the nonlinear partial differential equations. The anal- ysis shows that our analytical approximate solutions converge very rapidly to the exact solutions.