Journal of Nonlinear Mathematical Physics

Volume 3, Issue 1-2, May 1996, Pages 24 - 39

Lie Symmetries, Infinite-Dimensional Lie Algebras and Similarity Reductions of Certain (2+1)-Dimensional Nonlinear Evolution Equations

Authors
M. LAKSHMANAN, M. SENTHIL VELAN
Corresponding Author
M. LAKSHMANAN
Available Online 19 December 2006.
DOI
https://doi.org/10.2991/jnmp.1996.3.1-2.2How to use a DOI?
Abstract
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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
3 - 1
Pages
24 - 39
Publication Date
2006/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1996.3.1-2.2How 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. LAKSHMANAN
AU  - M. SENTHIL VELAN
PY  - 2006
DA  - 2006/12
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  - https://doi.org/10.2991/jnmp.1996.3.1-2.2
ID  - LAKSHMANAN2006
ER  -