On the solution of the nonlinear Korteweg-de Vries equation by the homotopy perturbation method

• Published in: Communications in numerical methods in engineering Vol. 25; no. 12; pp. 1127 - 1136
• Main Author: Yildirim, Ahmet
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.12.2009; Wiley
• Subjects: Computational techniques; Exact sciences and technology; Exact solutions; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; homotopy perturbation method; Iterative methods; Korteweg-de Vries equation; Mathematical analysis; Mathematical methods in physics; Mathematical models; nonlinear phenomena; Nonlinearity; Numerical analysis; Perturbation methods; Physics; Power series; Korteweg-de Vries equation; Homotopy; Perturbation techniques; Series expansion; homotopy perturbation method; Modelling; Non linear effect; Power series; Exact solution; nonlinear phenomena
• ISSN: 1069-8299; 2040-7947; 2040-7939; 1099-0887; 2040-7947
• DOI: 10.1002/cnm.1146

In this paper, the homotopy perturbation method is used to implement the nonlinear Korteweg–de Vries equation. The analytical solution of the equation is calculated in the form of a convergent power series with easily computable components. A suitable choice of an initial solution can lead to the needed exact solution by a few iterations. Copyright © 2008 John Wiley & Sons, Ltd.