Differential Equations and Nonlinear Mechanics
Volume 2009 (2009), Article ID 395894, 29 pages
doi:10.1155/2009/395894
Research Article

On Perturbative Cubic Nonlinear Schrodinger Equations under Complex Nonhomogeneities and Complex Initial Conditions

Magdy A. El-Tawil1 and Maha A. El-Hazmy2

1Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Giza 12613, Egypt
2Department of Mathematics, Girls College, Medina, Saudi Arabia

Received 12 February 2009; Revised 30 May 2009; Accepted 8 July 2009

Academic Editor: Roger Grimshaw

Copyright © 2009 Magdy A. El-Tawil and Maha A. El-Hazmy. 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

A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.