Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order

Gladwin Pradeep, R. ; Chandrasekar, V. K. ; Senthilvelan, M. ; Lakshmanan, M. (2011) Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order Journal of Physics A: Mathematical and General, 44 (44). p. 445201. ISSN 0305-4470

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Official URL: http://iopscience.iop.org/1751-8121/44/44/445201

Related URL: http://dx.doi.org/10.1088/1751-8113/44/44/445201

Abstract

In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs.

Item Type:Article
Source:Copyright of this article belongs to Institute of Physics.
ID Code:85048
Deposited On:29 Feb 2012 07:06
Last Modified:19 May 2016 01:15

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