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International Journal of Mathematical Analysis and Applications

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On Solution of Nonlinear Cubic Non-Homogeneous Schrodinger Equation with Limited Time Interval

International Journal of Mathematical Analysis and Applications
Vol.2 , No. 1, Publication Date: Apr. 21, 2015, Page: 9-16

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Authors

[1]	Sherif E. Nasr, Engineering Mathematics Department, Faculty of Engineering, Fayoum University, Fayoum, Egypt.
[2]	H. El Zoheiry, Engineering Mathematics Department, Faculty of Engineering, Cairo University, Giza, Egypt.

Abstract

In this paper, a perturbing nonlinear cubic non-homogeneous Schrodinger equation, i∂u(t,z)/∂z+α(∂^2 u(t,z))/(∂t^2 )+ε|u(t,z) |^2 u(t,z)+iγu(t,z)=F_1 (t,z)+iF_2 (t,z), (t,z)∈(0,T) x (0,∞) is studied under limited time interval, complex initial conditions and zero Neumann conditions. The perturbation method and Picard approximation 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 solution algorithm is tested through computing the possible orders of approximations. The method of solution is illustrated through case studies and figures. Effect of time interval (T) had been studied through cases studies and figures.

Keywords

Nonlinear Schrodinger Equation, Perturbation, Eigen function Expansion, Mathematica, Picard Approximation

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