AJCM  Vol.1 No.4 , December 2011
Analytical Solution of Two Extended Model Equations for Shallow Water Waves by He’s Variational Iteration Method
Abstract: In this paper, we consider two extended model equations for shallow water waves. We use He’s variational iteration method (VIM) to solve them. It is proved that this method is a very good tool for shallow water wave equations and the obtained solutions are shown graphically.
Cite this paper: nullM. Safari and M. Safari, "Analytical Solution of Two Extended Model Equations for Shallow Water Waves by He’s Variational Iteration Method," American Journal of Computational Mathematics, Vol. 1 No. 4, 2011, pp. 235-239. doi: 10.4236/ajcm.2011.14027.

[1]   P. A. Clarkson and E. L. Mansfield, “On a Shallow Water Wave Equation,” Nonlinearity, Vol. 7, No. 3, 1994, pp. 975-1000. doi:10.1088/0951-7715/7/3/012

[2]   M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur, “The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems,” Studies in Applied Mathematics, Vol. 53, 1974, pp.249-315.

[3]   R. Hirota and J. Satsuma,” Soliton Solutions of Model Equations for Shallow Water Waves,” Journal of the Physical Society of Japan, Vol. 40, No. 2, 1976, pp. 611- 612. doi:10.1143/JPSJ.40.611

[4]   J. H. He, “Some Asymptotic Methods for Strongly Nonlinear Equations,” International Journal of Modern Physics B, Vol. 20, No. 10, 2006, pp. 1141-1199. doi:10.1142/S0217979206033796

[5]   J. H. He, “Approximate Analytical Solution for Seepage Flow with Fractional Derivatives in Porous Media,” Com- puter Methods in Applied Mechanics and Engineering, Vol. 167, No. 1-2, 1998, pp. 57-68. doi:10.1016/S0045-7825(98)00108-X

[6]   J. H. He, “Variational Iteration Method for Autonomous Ordinary Differential Systems,” Applied Mathematics and Computation, Vol. 114, No. 2-3, 2000, pp. 115-123. doi:10.1016/S0096-3003(99)00104-6

[7]   J. H. He and X. H. Wu, “Construction of Solitary Solu- tion and Compacton-Like Solution by Variational Itera- tion Method,” Chaos Solitons & Fractals, Vol. 29, No. 1, 2006, pp. 108-113. doi:10.1016/j.chaos.2005.10.100

[8]   J. H. He, “A New Approach to Nonlinear Partial Differential Equations”, Communications in Nonlinear Science and Numerical Simulation, Vol. 2, No. 4, 1997, pp. 203- 205. doi:10.1016/S1007-5704(97)90007-1

[9]   J. H. He, “Variational Iteration Method—A Kind of Non- linear Analytical Technique: Some Examples,” Interna- tional Journal of Nonlinear Mechanics, Vol. 34, No. 4, 1999, pp. 699-708. doi:10.1016/S0020-7462(98)00048-1

[10]   J. H. He, “A Generalized Variational Principle in Micro- morphic Thermoelasticity,” Mechanics Research Commu- nications, Vol. 32, No. 1, 2005, pp. 93-98. doi:10.1016/j.mechrescom.2004.06.006

[11]   D. D. Ganji, M. Jannatabadi and E. Mohseni, “Applica- tion of He’s Variational Iteration Method to Nonlinear Jaulent-Miodek Equations and Comparing It with ADM,” Journal of Computional and Applied Mathematics, Vol. 207, No. 1, 2007, pp. 35-45.

[12]   D. D. Ganji, E. M. M. Sadeghi and M. Safari, “Appli- cation of He’s Variational Iteration Method and Ado- mian’s Decomposition Method Method to Prochhammer Chree Equation,” International Journal of Modern Phy- sics B, Vol. 23, No. 3, 2009, pp. 435-446. doi:10.1142/S0217979209049656

[13]   M. Safari, D. D. Ganji and M. Moslemi, “Application of He’s Variational Iteration Method and Adomian’s Decomposition Method to the Fractional KdV-Burgers- Kuramoto Equation,” Computers and Mathematics with Applications, Vol. 58, No. 11-12, 2009, pp. 2091-2097.

[14]   M. Safari, D. D. Ganji and E. M. M. Sadeghi, “Appli- cation of He’s Homotopy Perturbation and He’s Varia- tional Iteration Methods for Solution of Benney-Lin Equation,” International Journal of Computer Mathema- tics, Vol. 87, No. 8, pp. 1872-1884. doi:10.1080/00207160802524770

[15]   D. D. Ganji, M. Safari and R. Ghayor, “Application of He’s Variational Iteration Method and Adomian’s De- composition Method to Sawada-Kotera-Ito Seventh-Order Equation”, Numerical Methods for Partial Differential Equations, Vol. 27, No. 4, 2011, pp. 887-897. doi:10.1002/num.20559