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Analytical Solutions of Kortweg-de Vries(KdV) Equation
Abstract:The objective of this paper is to present a comparative study of Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM) for the semi analytical solution of Kortweg-de Vries (KdV) type equation called KdV. The study have been highlighted the efficiency and capability of aforementioned methods in solving these nonlinear problems which has been arisen from a number of important physical phenomenon.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1083205Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1896
 D.J. Korteweg, G. de Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave, Philos. Mag. Vol.39, 1895, pp. 422-443.
 Luwai Wazzan, A modified tanh-coth method for solving the KdV and the KdV-Burgers equations, Journal of Communication in nonlinear science and numerical simulation, (2007)
 A.J. Khattak, Siraj-ul-Islam, A comparative study of numerical solutions of a class of KdV equation , Journal of Computnational Applied Mathematical, Vol. 199, 2008 , pp.425-434.
 T. Ozis, S. Ozer S, A simple similarity-transformation-iterative scheme applied to Korteweg-de Vries equation, Journal of Applied Mathematical Compution, Vol. 173, 2006, pp.19-32.
 Abdul-Majid Wazwaz, The variational iteration method for rational solutions for KdV, K(2,2) Burgers and cubic Boussinesq equations, Journal of Computional Applied Mathematical, Article, (2006)
 P. Rosenau, J. M. Hyman, Compactons Solitons with finite wavelengths, Physics. Review Letter. Vol.70, No.5, 1993, pp. 564 -567.
 M.A. Abdou, A.A. Soliman, Variational iteration method for solving Burger's and coupled Burger's equation, Journal in Computensional Applied Mathematical, Vol.181, 2005, pp.245-251
 E.M. Aboulvafa, M.A. Abdou, A.A. Mahmoud, The solution of nonlinear coagulation problem with mass loss, Chaos Solitons And Fractals Vol.29, 2006, pp.313-330
 J.H. He, A new approach to nonlinear partial differential equations, Comm. Nonlinear Science and Numereical Simulation, Vol.2, No.4, 1997, pp.203-205.
 S.J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, PhD thesis Shanghai Jiao Tong University, 1992
 N. Tolou. I. Khatami. B. Jafari. D.D. Ganji. Analytical Solution of Nonlinear Vibrating Systems. American journal of applied Sciences, Vol.5, No.9, 2008, pp.1219-1224.
 M.J. Ablowitz, P.A. Clarkson, Solitions, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, 1991
 A. Coely, (Eds.), Backlund and Darboux Transformations, American Mathematical Society, Providence, Rhode Island, 2001
 M. Wadati, H. Sanuki, K. Konno, Relationships among inverse method, backlund transformation and an infinite number of conservation laws, Prog. Theoret. Phys. Vol.53, 1975, pp.419-436
 C.S. Gardner, J.M. Green, M.D. Kruskal, R.M. Miura, Method for solving the Korteweg-deVries equation, Phys. Rev. Lett. Vol.19, 1967, pp.1095-1097
 J.H. He, Homotopy perturbation method for bifurcation of nonlinear problems", Int. J. Non-linear Sci. Num. Sim., 6(2): 207-208 (2005)
 S.J. Liao, Beyond Perturbation: Introduction to the homotopy Analysis Method, Chapman & Hall/CRC press, Boca Raton, (2003)
 S. Abbasbandy, The application of homotopy analysis method to nonlinear equations arising in heat transfer, Phys. Lett. A