Author(s)

Abeer Al-Shareef¹, Alyaa A. Al Qarni², Safa Al-Mohalbadi¹, Huda O. Bakodah³

¹Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia.
²Department of Mathematics, Faculty of Science, Blqarn Campus, Bisha University, Bisha, Kingdom of Saudi Arabia.
³Department of Mathematics, Faculty of Science, Al Faisaliah Campus, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia.

In this paper, the improved Adomian decomposition method (ADM) is applied to the nonlinear Schrödinger’s equation (NLSE), one of the most important partial differential equations in quantum mechanics that governs the propagation of solitons through optical fibers. The performance and the accuracy of our improved method are supported by investigating several numerical examples that include initial conditions. The obtained results are compared with the exact solutions. It is shown that the method does not need linearization, weak or perturbation theory to obtain the solutions.

Nonlinear Differential Equation, Schrödinger Equation, Adomian Decomposition, Reliable Technique

Al-Shareef, A. , Al Qarni, A. , Al-Mohalbadi, S. and Bakodah, H. (2016) Soliton Solutions and Numerical Treatment of the Nonlinear Schrodinger’s Equation Using Modified Adomian Decomposition Method. Journal of Applied Mathematics and Physics, 4, 2215-2232. doi: 10.4236/jamp.2016.412215.