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Variational iteration method for solving coupled-KdV equations. (English) Zbl 1152.35466
Summary: In this paper, the He’s variational iteration method is applied to solve the non-linear coupled-KdV equations. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converge to the exact solution of the coupled-KdV equations. This procedure is a powerful tool for solving coupled-KdV equations.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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[1] Caom, D.B.; Yan, J.R.; Zang, Y., Exact solutions for a new coupled mkdv equations and a coupled KdV equations, Phys lett A, 297, 68-74, (2002) · Zbl 0994.35104
[2] Das, G.; Sarma, J., Response to comment on ’A new mathematical approach for finding the solitary waves in dusty plasma’, Phys plasmas, 6, 4394-4397, (1999)
[3] Gao, Y.T.; Tian, B., Ion-acoustic shocks in space and laboratory dusty plasmas: two-dimensional and non-traveling-wave observable effects, Phys plasmas, 8, 3146-3149, (2001)
[4] Ganji, D.D.; Rafei, M., Solitary wave solutions for a generalized hirota – satsuma coupled-KdV equation by homotopy perturbation method, Phys lett A, 356, 131-137, (2006) · Zbl 1160.35517
[5] Ganji DD, Jannatabadi M, Mohseni E. Application of He’s variational iteration method to nonlinear Jaulent-Miodek equations and comparing it with ADM. J Comput Appl Math, in press, Corrected proof, Available online 8 September (2006). · Zbl 1120.65107
[6] Hirota, R.; Satsuma, J., Solition solutions of a coupled Korteweg-de Vries equation, Phys lett A, 85, 407-408, (1981)
[7] He, J.H., Approximate analytical solution for seepage flow with fractional derivati in porous media, Comput methods appl mech eng, 167, 69-73, (1998)
[8] Hong, H.; Lee, H., Korteweg-de Vries equation of ion acoustic surface waves, Phys plasmas, 6, 3422-3424, (1999)
[9] He, J.H., Variational iteration method: a King of nonlinear analytical techniqe: some examples, Internat nonlinear mech, 344, 699-708, (1999)
[10] He, J.H., Approximate analytical methods in science and engineering, (2002), Henan Science and Technology press zheng zhou, in Chinese
[11] He, J.H., Generalized variational principles in fluids, (2003), Science and Culture Publishing House of China Hongkong, in Chinese · Zbl 1054.76001
[12] He, J.H.; Wu, X.H., Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, solutions & fractals, 29, 1, 108-113, (2006) · Zbl 1147.35338
[13] He, J.H., Some asymptotic methods for strongly nonlinear equations, Internat J mod phys B, 20, 10, 1141-1199, (2006) · Zbl 1102.34039
[14] Osborne, A., The inverse scattering transform: tools for the nonlinear Fourier analysis and filtering of Ocean surface waves, Chaos, solitons & fractals, 5, 2623-2637, (1995) · Zbl 1080.86502
[15] Ostrovsky, L.; Stepanyants, Yu.A., Do interal solutions exist in the Ocean?, Rev geophys, 27, 293-310, (1989)
[16] Sweilam, N.H.; Khader, M.M., Variational iteration method for one dimensional nonlinear thermoelasticity, Chaos, solitons & fractals, 32, 145-149, (2007) · Zbl 1131.74018
[17] Zayed, E.M.E.; Zedan, H.A.; Gepreel, K.A., On the solitary wave solutions for non-linear hirota – satsuma coupled-KdV of equations, Chaos, solitons & fractals, 22, 285-303, (2004) · Zbl 1069.35080
[18] Zhang, J.L.; Wang, M.L.; Feng, Z.D., The improved F-expansion method and its applications, Phys lett A, 350, 103-109, (2006) · Zbl 1195.65211
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