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.
Highlights
IntroductionThe governing equation for the propagation of optical solitons for trans-continental and trans-oceanic distances through an optical fiber is given by the nonlinear Schrödinger’s equation (NLSE) that can be derived from the Maxwell’s equation with the aid of multiple scale analysis
The study of optical solitons has been going on for the past few decades [1]-[10]
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
Summary
The governing equation for the propagation of optical solitons for trans-continental and trans-oceanic distances through an optical fiber is given by the nonlinear Schrödinger’s equation (NLSE) that can be derived from the Maxwell’s equation with the aid of multiple scale analysis. The Adomian decomposition method provides the solution in a rapid convergent series with computable terms. This method was successfully applied to nonlinear differential equations. Different modifications to solve nonlinear differential equations are given in [18] [19] [20]. The main goal of this paper is to apply some modifications of Adomian decomposition method to the nonlinear Schrödinger’s equation and compare the results with the exact solutions
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