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Application of the variational iteration method to the Whitham-Broer-Kaup equations. (English) Zbl 1138.76024
Summary: Using the variational iteration method, we obtain explicit traveling wave solutions of Whitham-Broer-Kaup equations including blow-up and periodic solutions. Moreover, the results are compared with those obtained by Adomian decomposition method, revealing that the variational iteration method is superior to Adomian decomposition method.

MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M30Variational methods (fluid mechanics)
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References:
[1] Whitham, G. B.: Variational methods and applications to water waves. Proceedings of the royal society of London, series A 299, 6-25 (1967) · Zbl 0163.21104
[2] Broer, L. J. F.: Approximate equations for long water waves. Applied scientific research 31, 377-395 (1975) · Zbl 0326.76017
[3] Kaup, D. J.: A higher-order water-wave equation and the method for solving it. Progress of theoretical physics 54, 396-408 (1975) · Zbl 1079.37514
[4] Kupershmidt, B. A.: Mathematics of dispersive water waves. Communications in mathematical physics 99, 51-73 (1985) · Zbl 1093.37511
[5] Ablowitz, M. J.; Clarkson, P. A.: Soliton, nonlinear evolution equations and inverse scattering. (1991) · Zbl 0762.35001
[6] Cox, D.: Ideal, varieties and algorithms. (1991)
[7] Whitham, G. B.: Linear and nonlinear waves. (1974) · Zbl 0373.76001
[8] Wang, M. L.; Zhou, Y.; Li, Z.: Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Physics letters A 216, 67-75 (1996) · Zbl 1125.35401
[9] Wang, M. L.: Solitary wave solutions for variant Boussinesq equations. Physics letters A 199, 169-172 (1995) · Zbl 1020.35528
[10] Yan, Z. Y.; Zhang, H. Q.: New explicit and exact traveling wave solutions for a system of variant Boussinesq equations in mathematical physics. Physics letters A 252, 291-296 (1999) · Zbl 0938.35130
[11] Xie, F.; Yan, Z.; Zhang, H. Q.: Explicit and exact traveling wave solutions of Whitham--Broer--Kaup shallow water equations. Physics letters A 285, 76-80 (2001) · Zbl 0969.76517
[12] He, J. H.: Variational iteration method for delay differential equations. Communications in nonlinear science and numerical simulation 2, No. 4, 235-236 (1997)
[13] He, J. H.: Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer methods in applied mechanics and engineering 167, 57-68 (1998) · Zbl 0942.76077
[14] He, J. H.: Approximate solution of nonlinear differential equations with convolution product nonlinearities. Computer methods in applied mechanics and engineering 167, 69-73 (1998) · Zbl 0932.65143
[15] He, J. H.: Variational iteration method -- a kind of nonlinear analytical technique: some examples. International journal of non-linear mechanics 34, 699-708 (1999) · Zbl 05137891
[16] He, J. H.; Wu, X. H.: Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, solitons and fractals 29, No. 1, 108-113 (2006) · Zbl 1147.35338
[17] He, J. H.: Variational iteration method for autonomous ordinary differential systems. Applied mathematics and computation 114, 115-123 (2000) · Zbl 1027.34009
[18] He, J. H.: Some asymptotic methods for strongly nonlinear equations. International journal of modern physics B 20, No. 10, 1141-1199 (2006) · Zbl 1102.34039
[19] Draganescu, G. E.; Capalnasan, V.: Nonlinear relaxation phenomena in polycrystalline solids. International journal of non-linear science and numerical simulation 4, No. 3, 219-225 (2003)
[20] Momani, S.; Abuasad, S.: Application of he’s variational iteration method to Helmholtz equation. Chaos, solitons and fractals 27, 1119-1123 (2006) · Zbl 1086.65113
[21] El-Sayed, S. M.; Kaya, D.: Exact and numerical traveling wave solutions of Whitham--Broer--Kaup equations. Applied mathematics and computation 167, 1339-1349 (2005) · Zbl 1082.65580