Document Type : Research Paper
Authors
Faculty of Mathematics Science, Department of Mathematics, Mazandaran University, P.O.Box 47415-95447, Babolsar, Iran
Abstract
Variational Iteration method using He's polynomials can be used to construct solitary solution and compacton-like solution for nonlinear dispersive equatioons. The chosen initial solution can be determined in compacton-like form or in solitary form with some compacton-like or solitary forms with some unknown parameters, which can be determined in the solution procedure. The compacton-like solution and solitary solution can be converted into each other.
Keywords
Main Subjects
[1] J. H. He, “Variational iteration method for autonomous ordinary differential systems”, Appl. Math. and Compu., Vol. 114, pp. 3115-3123, (2000).
[2] J. H. He and X. H. Wu, “Construction of solitary solution and compacton-like solution by variational iteration method”, Chao. Soli. Frac., Vol. 29, pp. 108-113, (2006).
[3] S. Momani and S. Abuasad, “Application of He's variational iteration method to Helmholtz equation” Chao. Soli. Frac., Vol. 27, pp. 115-123, (2006).
[4] Z. M. Odibat and S. Momani, “Application of variational iteration method to nonlinear differential equations of fractional order” Int. J. of Non. Sci. Numer. Simulat, Vol. 7, pp. 27-36, (2006).
[5] Mo. Miansari, D. D. Ganji and Me. Miansari, “Application of He's variational iteration method to nonlinear heat transfer equation”, Phys. Lett. A, Vol. 372, pp. 779-785, (2008).
[6] J. H. He, “Application of homotopy perturbation method to nonlinear wave equations”, Chao. Soli. Frac., Vol. 26, pp. 695-700, (2005).
[7] J. H. He, “Homotopy perturbation method for bifurcation of nonlinear problems”, Int. J. of Non. Sci. Numer. Simulat. Vol. 6, pp. 207-208, (2005).
[8] B. Ganjavi, H. Mohammadi, D. D. Ganji and A. Barari, “Homotopy pertubration method and variational iteration method for solving Zakharov-Kuznetsov equation”, Am. J. Appl .Sci., Vol. 5, pp. 811-817, (2008).
[9] S. Abbasbandy, “The application of homotopy analysis method to solve a generalized Hirota-Satsumal coupled Kdv equation” Phys. Lett. A, Vol. 361, pp. 478-483, (2007).
[10] A. K. Khalifa, K. R. Raslan and H. M. Alzubaidi, “Numerical study using the ADM for the modified regularized long wave equation”, Appl. Math., Modelling, Vol. 32, pp. 2962-2972, (2008).
[11] P. Rosenau and J. M. Hyman, “Compactons Solitons with finite wavelengths”, Phys. Rev. Lett., Vol. 75, pp. 564-567, (1993).
[12] P. Rosenau, “On nonanalytic solitary waves formed by a nonlinear dispersion”, Phys. Lett. A, Vol. 230, pp. 305-318, (1997).
[13] J. C. Saut, “Quelques généralisations de l'équation de Korteweg-de Vrie” , Journal of Differential Equations, Vol. 33, pp. 320-335, (1979).
[14] A. M. Wazwas, “Two reliable methods for solving variants of the KdV equation with compact and noncompact structure”, Chao. Soli. Frac., Vol. 28, pp. 767-776, (2006).
[15] S. M. Hassan and N.M. Alotaibi, “Solitary wave solutions of the improved Kdv equation by VIM”, Appl. Math. and Compu., Vol. 217, pp. 2397-2403, (2010).
[16] A. M. Wazwaz and M. A. Helal, “Variants of the generalized fifth-order KdV equation with compact and noncompact structures”, Chao. Soli. Frac., Vol. 21, pp. 579-589, (2004).
[17] A. M. Wazwaz, “Existence and construction of compacton solutions”, Chao. Soli. Frac., Vol. 19, pp. 463-470, (2004).
[18] Y. Zhu and X. Gao, “Exact special solitary solutions with compact support for the nonlinear dispersive K(m,n) equations”, Chao. Soli. Frac., Vol. 27, pp. 487-493, (2006).
[19] A. M. Wazwaz, “The variational iteration method: A reliable analytic tool for solving linear and nonlinear wave equations”, Comput. and Math. with Appl., Vol. 54, pp. 926-932, (2007).
[20] A. M. Wazwaz, “The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations”, J. Comput. Appl. Math., Vol. 207, pp. 18-23, (2007).
[21] J. Biazar, H. Ghazvini and M. Eslami, “He's homotopy perturbation method for systems of integro-differential equations”, Chaos, Solitons and Fractals, Vol. 39, pp. 1253-1258, (2009).
[22] J. H. He, “A coupling method of homotopy technique and perturbation technique for nonlinear problems”, Int. J. Nonlinear Mech., Vol. 35, pp. 37-43, (2000).
[23] J. H. He, “Homotopy perturbation method for solving boundary value problems”, Phys. Lett A., Vol. 350, pp. 87-88, (2006).
[24] J. H. He, “Some asymptotic methods for strongly nonlinear equations”, Int. J. Mod. Phys. B., Vol. 20 , pp. 1141-1199, (2006).
[25] J. H. He, “New Interpretation of homotopy-perturbation method”, Int. J. Mod. Phys. B., Vol. 20, pp. 2561-2568, (2006).
[26] A. Ghorbani, “Beyond Adomian polynomials: He polynomials”, Chaos Solitons Fractals, Vol. 39, pp. 1486-1492, (2009).
[27] S. T. Mahyud-Din and A. Yildirim, “Variational iteration method for delay differential equations using He's polynamials”, Zeitschrif Fur Naturforschung section A- J. of Phyisical Sci., Vol. 5, pp. 1045-1048, (2010).
[28] Y. Khan and Q. B. Wu, “Homotopy Perturbation transform method for nonlinear equations using He's polynamials”, Compu. and Math. with Application, Vol. 41, pp. 1963-1967, (2011).
[29] M. Matinfar, M. Mahdavi and Z. Raeisi, “The variational homotopy perturbation method for solving analytic treatment of the linear and nonlinear ordinary differential equations”, J. Appl. Math. and Informatics, Vol. 28, pp. 845-862, (2010).
[30] M. Matinfar and M. Ghasemi, “Variational Homotopy Perturbation Method for the Zakharove-Kuznetsov Equations”, J. of Math. and Statistics, Vol. 6, pp. 425-430, (2010).
[31] J. H. He and X. H. Wu, “Construction of solitary solution and compacton-like solution by variational iteration method”, Chao. Soli. Frac., Vol. 29, pp. 108-113, (2006).
[32] T. S. Al-Danaf, M. A. Ramadan and F. E. I. Abd- Alaal, “The use of adomian decomposition method for solving the regularized long-wave equation”, Chao. Soli. Frac., Vol. 26, pp. 747-757, (2005).
[33] A. T. Abassy, M. A. El-Tawil and H. K. Saleh, “The solution of KdV and mKdV equations using Adomian Pade Approximation”, Int. J. of Non. Sci. Numer. Simulat, Vol. 5, pp. 327-339, (2004).
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