- 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
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 741780, 7 pages
On the Solutions and Conservation Laws of a Coupled Kadomtsev-Petviashvili Equation
Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
Received 6 October 2012; Accepted 2 December 2012
Academic Editor: Asghar Qadir
Copyright © 2013 Chaudry Masood Khalique. 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.
- D. J. Korteweg and G. de Vries, “On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves,” Philosophical Magazine, vol. 39, pp. 422–443, 1895.
- A. M. Wazwaz, “Integrability of coupled KdV equations,” Central European Journal of Physics, vol. 9, no. 3, pp. 835–840, 2011.
- B. B. Kadomtsev and V. I. Petviashvili, “On the stability of solitary waves in weakly dispersive media,” Soviet Physics. Doklady, vol. 15, pp. 539–541, 1970.
- D.-S. Wang, “Integrability of a coupled KdV system: Painlevé property, Lax pair and Bäcklund transformation,” Applied Mathematics and Computation, vol. 216, no. 4, pp. 1349–1354, 2010.
- C.-X. Li, “A hierarchy of coupled Korteweg-de Vries equations and the corresponding finite-dimensional integrable system,” Journal of the Physical Society of Japan, vol. 73, no. 2, pp. 327–331, 2004.
- Z. Qin, “A finite-dimensional integrable system related to a new coupled KdV hierarchy,” Physics Letters A, vol. 355, no. 6, pp. 452–459, 2006.
- X. Geng, “Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations,” Journal of Physics A, vol. 36, no. 9, pp. 2289–2303, 2003.
- X. Geng and Y. Ma, “N-solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation,” Physics Letters A, vol. 369, no. 4, pp. 285–289, 2007.
- X. Geng and G. He, “Some new integrable nonlinear evolution equations and Darboux transformation,” Journal of Mathematical Physics, vol. 51, no. 3, Article ID 033514, 21 pages, 2010.
- A.-M. Wazwaz, “Integrability of two coupled kadomtsev-petviashvili equations,” Pramana, vol. 77, no. 2, pp. 233–242, 2011.
- 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. 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.
- S. C. Anco and G. Bluman, “Direct construction method for conservation laws of partial differential equations. I. Examples of conservation law classifications,” European Journal of Applied Mathematics, vol. 13, no. 5, pp. 545–566, 2002.
- M. Anthonyrajah and D. P. Mason, “Conservation laws and invariant solutions in the Fanno model for turbulent compressible flow,” Mathematical & Computational Applications, vol. 15, no. 4, pp. 529–542, 2010.
- G. W. Bluman and S. Kumei, Symmetries and Differential Equations, vol. 81 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989.
- R. Naz, F. M. Mahomed, and D. P. Mason, “Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics,” Applied Mathematics and Computation, vol. 205, no. 1, pp. 212–230, 2008.
- A. Sjöberg, “Double reduction of PDEs from the association of symmetries with conservation laws with applications,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 608–616, 2007.
- A. Sjöberg, “On double reductions from symmetries and conservation laws,” Nonlinear Analysis: Real World Applications, vol. 10, no. 6, pp. 3472–3477, 2009.
- A. H. Bokhari, A. Y. Al-Dweik, F. D. Zaman, A. H. Kara, and F. M. Mahomed, “Generalization of the double reduction theory,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 3763–3769, 2010.
- N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, vol. 1–3, CRC Press, Boca Raton, Fla, USA, 1996.
- A. F. Cheviakov, “GeM software package for computation of symmetries and conservation laws of differential equations,” Computer Physics Communications, vol. 176, no. 1, pp. 48–61, 2007.