Geometrical interpretation and approximate solution of non-linear KdV equation

Purpose - The purpose is to study an analytical solution of non-linear Korteweg-de Vries (KdV) equation by using the Adomian decomposition method (ADM).Design methodology approach - The solution is calculated in the form of a series with easily computable components. The non-linear KdV equation has...

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Bibliographic Details
Published in:Kybernetes 2005-08, Vol.34 (7/8), p.941-950
Main Authors: Bektas, M, Inc, M, Cherruault, Y
Format: Article
Language:English
Subjects:
Cybernetics
Geometry
Mathematical analysis
Nonlinear equations
Polynomials
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Summary:Purpose - The purpose is to study an analytical solution of non-linear Korteweg-de Vries (KdV) equation by using the Adomian decomposition method (ADM).Design methodology approach - The solution is calculated in the form of a series with easily computable components. The non-linear KdV equation has been considered and the analytic solution is compared with its numerical solution by using the ADM and Mathematica software program.Findings - This approach to the non-linear evolution equation was found to be valuable as a tool for scientists and applied mathematicians, because it provides immediate and visible symbolic terms of analytical solution as well as its numerical approximate solution to both linear and non-linear problems without linearization or discretization.Research limitations implications - This geometrical interpretation and the produced approximate solution of the non-linear KdV equation illustrates the use of the ADM. Research using ADM is ongoing but already the numerical results obtained in this paper justify the advantages of this methodology, even in a few terms of approximation.Practical implications - Using the Mathematica software package the ADM was implemented for homogenous KdV equation as an illustrative example which has distinct applications for scientists and applied mathematicians.Originality value - This is an original study of the use of ADM for the solution of the non-linear KdV equation. It also shows how the Mathematica software package can be used in such studies.
ISSN:0368-492X
1758-7883
DOI:10.1108/03684920510605768