Pandey, S. N. ; Bindu, P. S. ; Senthilvelan, M. ; Lakshmanan, M. (2009) A group theoretical identification of integrable cases of the Lienard-type equation x···+f(x) x···+g(x) = 0. I. Equations having nonmaximal number of Lie point symmetries Journal of Mathematical Physics, 50 (8). 082702_1-082702_19. ISSN 0022-2488
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Official URL: http://jmp.aip.org/resource/1/jmapaq/v50/i8/p08270...
Related URL: http://dx.doi.org/10.1063/1.3187783
Abstract
We carry out a detailed Lie point symmetry group classification of the Lienard-type equation, x···+f(x) x···+g(x) = 0, where f(x) and g(x) are arbitrary smooth functions of x. We divide our analysis into two parts. In the present first part we isolate equations that admit lesser parameter Lie point symmetries, namely, one, two, and three parameter symmetries, and in the second part we identify equations that admit maximal (eight) parameter Lie point symmetries. In the former case the invariant equations form a family of integrable equations, and in the latter case they form a class of linearizable equations (under point transformations). Further, we prove the integrability of all the equations obtained in the present paper through equivalence transformations either by providing the general solution or by constructing time independent Hamiltonians. Several of these equations are being identified for the first time from the group theoretical analysis.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Institute of Physics. |
Keywords: | Group Theory; Integral Equations; Lie Algebras; Lie Groups; Symmetry |
ID Code: | 85028 |
Deposited On: | 29 Feb 2012 07:02 |
Last Modified: | 29 Feb 2012 07:02 |
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