Lott, D.A., Henriquez, A., Sturdevant, B.J.M. and Biswas, A. (2009) A Numerical Study of Optical Soliton-Like Structures Resulting from the Nonlinear Schrödinger’s Equation with Square-Root Law Nonlinearity. Mathematics and Computation, 207, 319-326.
https://doi.org/10.1016/j.amc.2008.10.038

has been cited by the following article:

• TITLE: Soliton Solutions and Numerical Treatment of the Nonlinear Schrodinger’s Equation Using Modified Adomian Decomposition Method

  AUTHORS: Abeer Al-Shareef, Alyaa A. Al Qarni, Safa Al-Mohalbadi, Huda O. Bakodah

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.12, December 26, 2016

  ABSTRACT: 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.