Research ArticleOpen AccessGoogle Scholar indexed
Analytical Solution of Two Extended Model Equations for Shallow Water Waves by He’s Variational Iteration Method
- 1
- 2
American Journal of Computational Mathematics·Volume 01 (2011)·Pages 235–239·Published 22 December 2011·DOI10.4236/ajcm.2011.14027
Copy link · social · email
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.
KeywordsHe’s Variational Iteration MethodShallow Water Wave Equation
- 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
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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.
- 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