Lie Symmetries, Kac-Moody-Virasoro Algebras and Integrability of Certain (2+1)-Dimensional Nonlinear Evolution Equations
作者:
M. Senthil Velan,
M. Lakshmanan,
期刊:
Journal of Nonlinear Mathematical Physics
(Taylor Available online 1998)
卷期:
Volume 5,
issue 2
页码: 190-211
ISSN:1402-9251
年代: 1998
DOI:10.2991/jnmp.1998.5.2.10
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
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 Schrüdinger 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.
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