- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 350287, 7 pages
Exact Solutions of Equation Using Lie Symmetry Approach along with the Simplest Equation and Exp-Function Methods
1Department of Mathematics Science, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran
2International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
Received 21 August 2012; Revised 22 October 2012; Accepted 9 November 2012
Academic Editor: Lan Xu
Copyright © 2012 Hossein Jafari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. Duranda and D. Langevin, “Physicochemical approach to the theory of foam drainage,” The European Physical Journal E, vol. 7, pp. 35–44, 2002.
- E. Fan, “Extended tanh-function method and its applications to nonlinear equations,” Physics Letters A, vol. 277, no. 4-5, pp. 212–218, 2000.
- L. A. Ostrovsky, “Nonlinear internal waves in a rotating ocean,” Oceanology, vol. 18, pp. 119–125, 1978.
- A.-M. Wazwaz, “The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1467–1475, 2007.
- A.-M. Wazwaz, “The tanh method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations,” Chaos, Solitons & Fractals, vol. 25, no. 1, pp. 55–63, 2005.
- A.-M. Wazwaz, “The sine-cosine method for obtaining solutions with compact and noncompact structures,” Applied Mathematics and Computation, vol. 159, no. 2, pp. 559–576, 2004.
- R. Abazari, “Application of -expansion method to travelling wave solutions of three nonlinear evolution equation,” Computers & Fluids, vol. 39, no. 10, pp. 1957–1963, 2010.
- E. Salehpour, H. Jafari, and N. Kadkhoda, “Application of, -expansion method to nonlinear Lienard equation,” Indian Journal of Science and Technology, vol. 5, pp. 2554–2556, 2012.
- H. Jafari, N. Kadkhoda, and C. M. Khalique, “Travelling wave solutions of nonlinear evolution equations using the simplest equation method,” Computers & Mathematics with Applications, vol. 64, no. 6, pp. 2084–2088, 2012.
- N. A. Kudryashov, “Simplest equation method to look for exact solutions of nonlinear differential equations,” Chaos, Solitons & Fractals, vol. 24, no. 5, pp. 1217–1231, 2005.
- N. A. Kudryashov and N. B. Loguinova, “Extended simplest equation method for nonlinear differential equations,” Applied Mathematics and Computation, vol. 205, no. 1, pp. 396–402, 2008.
- N. K. Vitanov, “Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2050–2060, 2010.
- J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700–708, 2006.
- X.-H. Wu and J.-H. He, “EXP-function method and its application to nonlinear equations,” Chaos, Solitons & Fractals, vol. 38, no. 3, pp. 903–910, 2008.
- X. W. Zhou, Y. X. Wen, and J. H. He, “Exp-function method to solve the non-linear dispersive K(m,n) equations,” International Journal of Nonlinear Science and Numerical Simulation, vol. 9, pp. 301–306, 2008.
- G. W. Bluman and S. Kumei, Symmetries and Differential Equations, vol. 81 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989.
- N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, vol. 1–3, CRC Press, Boca Raton, Fla, USA, 19941996.
- A. G. Johnpillai and C. M. Khalique, “Lie group classification and invariant solutions of mKdV equation with time-dependent coefficients,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1207–1215, 2011.
- P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107 of Graduate Texts in Mathematics, Springer, Berlin, Germany, 2nd edition, 1993.