Differential Equations and Nonlinear Mechanics
Volume 2009 (2009), Article ID 395894, 29 pages
doi:10.1155/2009/395894
On perturbative cubic nonlinear Schrödinger 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
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.