Journal of Nonlinear Mathematical Physics

Volume 5, Issue 2, May 1998, Pages 190 - 211

Lie Symmetries, Kac-Moody-Virasoro Algebras and Integrability of Certain (2+1)-Dimensional Nonlinear Evolution Equations

Authors
M. SENTHIL VELAN, M. LAKSHMANAN
Corresponding Author
M. SENTHIL VELAN
Available Online 1 May 1998.
DOI
https://doi.org/10.2991/jnmp.1998.5.2.10How to use a DOI?
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 Schrödinger 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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
5 - 2
Pages
190 - 211
Publication Date
1998/05
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1998.5.2.10How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - M. SENTHIL VELAN
AU  - M. LAKSHMANAN
PY  - 1998
DA  - 1998/05
TI  - Lie Symmetries, Kac-Moody-Virasoro Algebras and Integrability of Certain (2+1)-Dimensional Nonlinear Evolution Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 190
EP  - 211
VL  - 5
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1998.5.2.10
DO  - https://doi.org/10.2991/jnmp.1998.5.2.10
ID  - VELAN1998
ER  -