Lie Symmetries, Infinite-Dimensional Lie Algebras and Similarity Reductions of Certain (2+1)-Dimensional Nonlinear Evolution Equations
- 10.2991/jnmp.1996.3.1-2.2How to use a DOI?
The Lie point symmetries associated with a number of (2 + 1)-dimensional generalizations of soliton equations are investigated. These include the Niznik Novikov Veselov equation and the breaking soliton equation, which are symmetric and asymmetric generalizations respectively of the KDV equation, the (2+1)-dimensional generalization of the nonlinear Schrödinger equation by Fokas as well as the (2+1)dimensional generalized sine-Gordon equation of Konopelchenko and Rogers. We show that in all these cases the Lie symmetry algebra is infinite-dimensional; however, in the case of the breaking soliton equation they do not possess a centerless Virasorotype subalgebra as in the case of other typical integrable (2+1)-dimensional evolution equations. We work out the similarity variables and special similarity reductions and investigate them.
- © 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/).
Cite this article
TY - JOUR AU - M. Lakshmanan AU - M. Senthil Velan PY - 1996 DA - 1996/05/01 TI - Lie Symmetries, Infinite-Dimensional Lie Algebras and Similarity Reductions of Certain (2+1)-Dimensional Nonlinear Evolution Equations JO - Journal of Nonlinear Mathematical Physics SP - 24 EP - 39 VL - 3 IS - 1-2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.1996.3.1-2.2 DO - 10.2991/jnmp.1996.3.1-2.2 ID - Lakshmanan1996 ER -