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

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

2011-09-27

arxiv.org/abs/1109.5777v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Accepted for publication in J. Phys. A Math. Theor. 2011

Scientific paper

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 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.

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