Lie Symmetries, Infinite-Dimensional Lie Algebras and Similarity Reductions of Certain (2+1)-Dimensional Nonlinear Evolution Equations
作者:
M. Lakshmanan,
M. Senthil Velan,
期刊:
Journal of Nonlinear Mathematical Physics
(Taylor Available online 1996)
卷期:
Volume 3,
issue 1-2
页码: 24-39
ISSN:1402-9251
年代: 1996
DOI:10.2991/jnmp.1996.3.1-2.2
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
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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