Senthil Velan, M. ; Lakshmanan, Muthusamy (1998) Lie symmetries, Kac-Moody-Virasoro algebras and integrability of certain (2+1)-dimensional nonlinear evolution equations Journal of Nonlinear Mathematical Physics, 5 (2). pp. 190-211. ISSN 1402-9251
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Official URL: http://www.atlantis-press.com/publications/jnmp/
Abstract
In this paper we study Lie symmetries, Kac-Moody-Virasoro algebras, similarity reductions and particular solutions of two different recently introduced (2+1)-dimensional nonlinear evolution equations, namely (i) (2+1)-dimensional breaking soliton equation and (ii) (2+1)-dimensional nonlinear Schr\"odinger type equation introduced by Zakharov and studied later by Strachan. Interestingly our studies show that not all integrable higher dimensional systems admit Kac-Moody-Virasoro type sub-algebras. Particularly the two integrable systems mentioned above do not admit Virasoro type subalgebras, eventhough the other integrable higher dimensional systems do admit such algebras which we have also reviewed in the Appendix. Further, we bring out physically interesting solutions for special choices of the symmetry parameters in both the systems.
Item Type: | Article |
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Source: | Copyright of this article belongs to Atlantis Press. |
ID Code: | 85008 |
Deposited On: | 29 Feb 2012 06:48 |
Last Modified: | 19 May 2016 01:13 |
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