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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.12 P.2079-2082

http://doi.org/10.1631/jzus.2006.A2079


Artificial perturbation for solving the Korteweg-de Vries equation


Author(s):  KHELIL N., BENSALAH N., SAIDI H., ZERARKA A.

Affiliation(s):  Laboratory of Physics and Applied Mathematics, University Med Khider, BP 145, 07000 Biskra, Algeria

Corresponding email(s):   azerarka@hotmail.com

Key Words:  Perturbation, Taylor series, Quintic spline, Korteweg-de Vries (KdV) equation


KHELIL N., BENSALAH N., SAIDI H., ZERARKA A.. Artificial perturbation for solving the Korteweg-de Vries equation[J]. Journal of Zhejiang University Science A, 2006, 7(12): 2079-2082.

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author="KHELIL N., BENSALAH N., SAIDI H., ZERARKA A.",
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DOI - 10.1631/jzus.2006.A2079


Abstract: 
A perturbation method is introduced in the context of dynamical system for solving the nonlinear korteweg-de Vries (KdV) equation. Best efficiency is obtained for few perturbative corrections. It is shown that, the question of convergence of this approach is completely guaranteed here, because a limited number of term included in the series can describe a sufficient exact solution. Comparisons with the solutions of the quintic spline, and finite difference are presented.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[3] El-Zoheiry, H., Iskandar, L., El-Naggar, B., 1994. The quintic spline for solving the Korteweg-de Vries equation. Mathematics and Computers in Simulation, 37(6):539-549.

[4] Fang, J.Q., Yao, W.G., 1992. Adomian’s Decomposition Method for the Solution of Generalized Duffing Equations. Proc. Internat. Workshop on Mathematics Mechanization, Beijing, China.

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[7] Gardner, C.S., Green, J.M., Kruskal, M.D., Miura, R.M., 1967. Method for solving the KdV equation. Phys. Rev. Lett., 19(19):1095-1097.

[8] Hirota, R., 1971. Exact solution of KdV equation for multiple collisions of solitons. Phys. Rev. Lett., 27(18):1192-1194.

[9] Iskandar, L., 1989. New numerical solution of the Korteweg-de Vries equation. Appl. Num. Math., 5(3):215-221.

[10] Korteweg, D.J., de Vries, G., 1895. On the change of the form of long waves advancing in a rectangular canal and on a new type of long stationary waves. Philos. Mag., 39:422-443.

[11] Tang, T., Xue, W.M., Zhang, P.W., 2001. Analysis of moving mesh methods based on geometrical variables. J. of Comp. Math., 19(1):41-54.

[12] Scott, A.C., Chu, E.Y.F., McLaughlin, D.W., 1973. The soliton: A new concept in applied science. Proc. of IEEE, 61:1443-1483.

[13] Zerarka, A., 1996. Solution of Korteweg-de Vries Equation by Decomposition Method. Internat. Cong. on Math. Appl. and Ingeen. Sc., Casablanca.

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