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El-Kalla, I.L. (2010) New Results on the Analytic Summation of Adomian Series for Some Classes of Differential and Integral Equations. Applied Mathematics and Computation, 217, 3756-3763.
https://doi.org/10.1016/j.amc.2010.09.034

has been cited by the following article:

• TITLE: A Comprehensive Study of Soliton Pulse Propagation Using Modified Differential Transform Methods

  AUTHORS: Entsar El-Shazly, Ahmed Abo-Elenin, Ibrahim El-Kalla

  KEYWORDS: Soliton Pulse, Parabolic Law Medium, Differential Transform Method, Bright Solution, Dark Solution, Schrödinger Equation, Radhakrishnan-Kundu-Laksmannan

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.12, December 26, 2024

  ABSTRACT: In this article, a modified version of the Differential Transform Method (DTM) is employed to examine soliton pulse propagation in a weakly non-local parabolic law medium and wave propagation in optical fibers. This semi-analytic method has the advantage of overcoming the obstacle of the hardest nonlinear terms and is used to explain the origin of the bright and dark soliton solutions through the Schrödinger equation in its non-local form and the Radhakrishnan-Kundu-Laksmannan (RKL) equation. Numerical examples demonstrate the effectiveness of this method.