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

In this paper, a perturbing nonlinear Schrodinger equation is studied under limited time interval through homo- geneous boundary conditions and real initial condition. The analytical solution for the linear case is introduced. The per- turbation 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.