The Open Applied Mathematics Journal

2008, 2 : 1-7
Published online 2008 March 08. DOI: 10.2174/1874114200802010001
Publisher ID: TOAMJ-2-1

On The Analytical Solution of Perturbative Nonlinear Schrodinger Equations with Real Initial and Homogeneous Boundary Conditions

Maha A. El-Hazmy
Girls college, Mathematics Department, Medina, P.O.B. 3193; Saudi Arabia.

ABSTRACT

In this paper, a perturbing nonlinear Schrodinger equation is studied under limited time interval through homogeneous boundary conditions and real initial condition. The analytical solution for the linear case is introduced. The perturbation method is used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the solution algorithm is tested through first order approximation. The method of solution is illustrated through case studies and figures.

Keywords:

Nonlinear Schrodinger equation, Perturbation, Eigenfunction expansion.