- 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 342680, 12 pages
Lie Groups Analysis and Contact Transformations for Ito System
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80303, Jeddah 21589, Saudi Arabia
Received 12 May 2012; Accepted 10 September 2012
Academic Editor: Ahmed El-Sayed
Copyright © 2012 M. M. Al-Shomrani. 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.
- H.-W. Tam, X.-B. Hu, and D.-L. Wang, “Two integrable coupled nonlinear systems,” Journal of the Physical Society of Japan, vol. 68, no. 2, pp. 369–379, 1999.
- A. Karasu-Kalkanli, A. Karasu, and S. Yu. Sakovich, “Integrability of a generalized Ito system: the Painlevé test,” Journal of the Physical Society of Japan, vol. 70, no. 5, pp. 1165–1166, 2001.
- M. Ito, “An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher orders,” Journal of the Physical Society of Japan, vol. 49, no. 2, pp. 771–778, 1980.
- G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer, New York, NY, USA, 1989.
- E. Momoniat and F. M. Mahomed, “The existence of contact transformations for evolution-type equations,” Journal of Physics A, vol. 32, no. 49, pp. 8721–8730, 1999.
- L. Hanze and J. Li, “Lie symmetry analysis and exact solutions for the extended mKdV equation,” Acta Applicandae Mathematicae, vol. 10, pp. 9362–9368, 2008.
- S. Shen, “Lie symmetry analysis and Painlevé analysis of the new -dimensional KdV equation,” Applied Mathematics B, vol. 22, no. 2, pp. 207–212, 2007.
- A. G. Johnpillai, C. M. Khalique, and A. Biswas, “Exact solutions of the mKdV equation with time-dependent coefficients,” Mathematical Communications, vol. 16, no. 2, pp. 509–518, 2011.
- G. W. Bluman and J. D. Cole, Similarity Methods for Differential Equations, Springer, Berlin, Germany, 1974.
- H. A. Zedan and S. M. Al-Tuwairqi, “Painleve analysis of generalized Zakharov equations,” Pacific Journal of Mathematics, vol. 247, no. 2, pp. 497–510, 2010.
- H. A. Zedan, “Symmetry analysis of an integrable Ito coupled system,” Computers & Mathematics with Applications, vol. 60, no. 12, pp. 3088–3097, 2010.
- H. A. Zedan, “Exact solutions for the generalized KdV equation by using Backlund transformations,” Journal of the Franklin Institute, vol. 348, no. 8, pp. 1751–1768, 2011.
- A. G. Johnpillai, A. H. Kara, and A. Biswas, “Symmetry solutions and reductions of a class of generalized (2+1)-dimenional Zakharov-Kuznetsov equation,” International Journal of Nonlinear Science and Numerical Simulation, vol. 12, no. 1–8, pp. 35–43, 2011.
- A. G. Johnpillai, A. Yildirim, and A. Biswas, “Chiral solutions with boham potential by Lie group analysis and travelling wave hypothesis,” Romanian Journal of Physics, vol. 57, no. 3-4, pp. 545–554, 2012.
- G. Ebadi , A. H. Kara , M. D. Petkovic, A. Yildirim, and A. Biswas, “Soliton solutions and conservation laws of Ito equation,” Proceedings of the Romanian Academy of Science A, vol. 13, no. 3, pp. 215–224, 2012.