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

DOI

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - M. Lakshmanan
AU  - M. Senthil Velan
PY  - 1998
DA  - 1998/05/01
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  - 10.2991/jnmp.1998.5.2.10
ID  - Lakshmanan1998
ER  -