Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 531823, 14 pages
http://dx.doi.org/10.1155/2012/531823
Research Article

Solution of ( 𝟑 + 𝟏 )-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method

Hassan A. Zedan1,2 and M. Ali Alghamdi1

1Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Kafr El-Sheikh University, Kafr El-Sheikh 33516, Egypt

Received 15 September 2011; Accepted 8 December 2011

Academic Editor: Xing-Gang Yan

Copyright © 2012 Hassan A. Zedan and M. Ali Alghamdi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.