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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 765361, 12 pages
Wave Equations in Bianchi Space-Times
1Centre for Differential Equations, Continuum Mechanics, and Applications, School of Mathematics, University of the Witwatersrand, Johannesburg 2001, South Africa
2School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041, South Africa
Received 31 July 2012; Accepted 26 September 2012
Academic Editor: Fazal M. Mahomed
Copyright © 2012 S. Jamal 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.
- S. Anco and G. B. luman, “Direct construction method for conservation laws of partial differential equations—part I: examples of conservation law classifications,” European Journal of Applied Mathematics, vol. 13, pp. 567–585, 2002.
- N. H. Ibragimov, Ed., CRC Handbook of Lie Group Analysis of Differential Equations: Symmetries, Exact Solutions and Conservation Laws, CRC Press, Boca Raton, Fla, USA, 1994.
- N. H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, vol. 4, John Wiley & Sons, Chichester, UK, 1999.
- P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107, Springer, New York, NY, USA, 2nd edition, 1993.
- L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, NY, USA, 1982.
- E. Noether, “Invariante variations probleme,” Nachrichten der Akademie der Wissenschaften in Göttingen, Mathematisch-Physikalische Klasse, vol. 2, p. 235, 1918, English translation in: Transport Theory and Statistical Physics, vol. 1, no. 3, p. 186, 1971.
- A. H. Bokhari and A. H. Kara, “Noether versus Killing symmetry of conformally flat Friedmann metric,” General Relativity and Gravitation, vol. 39, no. 12, pp. 2053–2059, 2007.
- A. H. Bokhari, A. H. Kara, A. R. Kashif, and F. D. Zaman, “Noether symmetries versus Killing vectors and isometries of spacetimes,” International Journal of Theoretical Physics, vol. 45, no. 6, pp. 1029–1039, 2006.
- A. H. Bokhari, A. Y. Al-Dweik, A. H. Kara, M. Karim, and F. D. Zaman, “Wave equation on spherically symmetric Lorentzian metrics,” Journal of Mathematical Physics, vol. 52, no. 6, 11 pages, 2011.
- S. Capozziello, G. Marmo, C. Rubano, and P. Scudellaro, “Nöther symmetries in Bianchi universes,” International Journal of Modern Physics D, vol. 6, no. 4, pp. 491–503, 1997.
- U. Camci and Y. Kucukakca, “Noether gauge symmetry for f(R) gravity in Palatini formalism,” Physical Review D, vol. 76, no. 8, Article ID 084023, 2007.
- A. K. Sanyal, “Bianchi type I cosmology in generalized Saez-Ballester theory via Noether gauge symmetry,” Physics Letters B, vol. 524, p. 177, 2002.
- I. M. Anderson and T. E. Duchamp, “Variational principles for second-order quasilinear scalar equations,” Journal of Differential Equations, vol. 51, no. 1, pp. 1–47, 1984.
- I. M. Anderson and T. Duchamp, “On the existence of global variational principles,” American Journal of Mathematics, vol. 102, no. 5, pp. 781–868, 1980.
- N. H. Ibragimov, Transformation Groups Applied to Mathematical Physics, D. Reidel Publishing, Dordrecht, The Netherlands, 1985.
- N. H. Ibragimov, A. H. Kara, and F. M. Mahomed, “Lie-Bäcklund and Noether symmetries with applications,” Nonlinear Dynamics, vol. 15, no. 2, pp. 115–136, 1998.
- S. Jamal, A. H. Kara, and A. H. Bokhari, “Symmetries, conservation laws and reduction of wave and Gordon-type equations on Riemannian manifolds,” in Proceedings of the International Conference on Applied Mathematics and Engineering (WASET '11), vol. 60, pp. 945–957, World Academy of Science, Engineering and Technology, Puket, Thailand, 2011.