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Variational iteration method for solving non-linear partial differential equations. (English) Zbl 1197.35227
Summary: We shall use the variational iteration method to solve some problems of non-linear partial differential equations (PDEs) such as the combined KdV-MKdV equation and Camassa-Holm equation. The variational iteration method is superior than the other non-linear methods, such as the perturbation methods where this method does not depend on small parameters, such that it can fined wide application in non-linear problems without linearization or small perturbation. In this method, the problems are initially approximated with possible unknowns, then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35A25Other special methods (PDE)
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References:
[1] Inokuti, M.: General use of the Lagrange multiplier in non-linear mathematical physics, Variational method in the mechanics of solids, 156-162 (1978)
[2] He, J. H.: Semi-inverse method of establishing generalized principles for fluid mechanics with emphasis on turbo-machinery aero dynamics, Int J turbo jet-engines 14, No. 1, 23-28 (1994)
[3] Finlayson, B. A.: The method of weighted residuals and variational principles, (1972) · Zbl 0319.49020
[4] He, J. H.: A new approach to non-linear partial differential equations, Commun non-linear sci numer simulat 2, No. 4, 230-235 (1997) · Zbl 0923.35046 · doi:10.1016/S1007-5704(97)90029-0
[5] He, J. H.: Variational iteration method for delay differential equations, Commun non-linear sci numer simulat 2, No. 4, 235-236 (1997) · Zbl 0924.34063
[6] He, J. H.: Variational iteration method for non-linearity and its applications, Mech practice 20, No. 1, 30-32 (1998)
[7] He, J. H.: Variational iteration -- a kind of non-linear analytical technique: some examples, Pergamon int J non-linear mech 34, 699-708 (1999) · Zbl 05137891
[8] Momani, Shaher.; Abuasad, Salah: Application of he’s variational iteration method to Helmholtz equation, Chaos solitons & fractals 27, 1119-1123 (2006) · Zbl 1086.65113 · doi:10.1016/j.chaos.2005.04.113
[9] Fan, Engui: Uniformly constructing a series of explicit exact solutions to non-linear equations in mathematical physics, Chaos solitons & fractals 16, 819-839 (2003) · Zbl 1030.35136 · doi:10.1016/S0960-0779(02)00472-1
[10] Mohamad, M. N. B.: Exact solutions to the combined KdV -- mkdv equation, Math methods appl sci 15, 73-80 (1992) · Zbl 0741.35071 · doi:10.1002/mma.1670150202
[11] Fuchssteiner, B.: Some tricks from the symmetry-toolbox for non-linear equations: generalizations of the Camassa -- Holm equation, Physica D 95, 229-243 (1996) · Zbl 0900.35345 · doi:10.1016/0167-2789(96)00048-6