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
M. SENTHIL VELAN, M. LAKSHMANAN
M. SENTHIL VELAN
Available Online 1 May 1998.
- https://doi.org/10.2991/jnmp.1922.214.171.124How to use a DOI?
- 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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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.19126.96.36.199 DO - https://doi.org/10.2991/jnmp.19188.8.131.52 ID - VELAN1998 ER -