title: |
Lie Symmetries, Infinite-Dimensional Lie Algebras and Similarity Reductions of Certain (2+1)-Dimensional Nonlinear Evolution Equations |
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publication: |
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| volume-issue: | 3 - 1-2 | |
| pages: | 24 - 39 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.1996.3.1-2.2 (how to use a DOI) | |
author(s): |
M. LAKSHMANAN, M. SENTHIL VELAN |
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publication date: |
May 1996 |
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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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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |