- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Mathematical Physics
Volume 2013 (2013), Article ID 591852, 8 pages
Some General New Einstein Walker Manifolds
1School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran
2Department of Complementary Education, Payame Noor University, Tehran 19395-3697, Iran
Received 1 October 2012; Accepted 7 November 2012
Academic Editor: Anatol Odzijewicz
Copyright © 2013 Mehdi Nadjafikhah and Mehdi Jafari. 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. Lie, “On integration of a class of linear partial differential equations by means of definite integrals,” Archiv der Mathematik, vol. 6, no. 3, pp. 328–368, 1881, translation by N. H. Ibragimov.
- P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1986.
- G. W. Bluman and J. D. Cole, Similarity Methods for Differential Equations, vol. 13 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1974.
- G. W. Bluman and S. Kumei, Symmetries and Differential Equations, vol. 81 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989.
- P. J. Olver and P. Rosenau, “Group-invariant solutions of differential equations,” SIAM Journal on Applied Mathematics, vol. 47, no. 2, pp. 263–278, 1987.
- R. Z. Zhdanov, I. M. Tsyfra, and R. O. Popovych, “A precise definition of reduction of partial differential equations,” Journal of Mathematical Analysis and Applications, vol. 238, no. 1, pp. 101–123, 1999.
- G. Cicogna, “A discussion on the different notions of symmetry of differential equations,” Proceedings of Institute of Mathematics of NAS of Ukraine, vol. 50, pp. 77–84, 2004.
- G. W. Bluman and J. D. Cole, “The general similarity solution of the heat equation,” Journal of Mathematics and Mechanics, vol. 18, pp. 1025–1042, 1969.
- M. Brozos-Vázquez, E. García-Río, P. Gilkey, S. Nikčević, and R. Vázquez-Lorenzo, The Geometry of Walker Manifolds, vol. 5 of Synthesis Lectures on Mathematics and Statistics Series, Morgan & Claypool, 2009.
- A. G. Walker, “Canonical form for a Riemannian space with a parallel field of null planes,” The Quarterly Journal of Mathematics, vol. 1, no. 2, pp. 69–79, 1950.
- M. Nadjafikhah and V. Shirvani-Sh, “Lie symmetry analysis of Kudryashov-Sinelshchikov equation,” Mathematical Problems in Engineering, vol. 2011, Article ID 457697, 9 pages, 2011.
- L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, NY, USA, 1982.
- M. Nadjafikhah, “Lie symmetries of inviscid Burgers' equation,” Advances in Applied Clifford Algebras, vol. 19, no. 1, pp. 101–112, 2009.