Sundman Symmetries of Nonlinear Second-Order and Third-Order Ordinary Differential Equations

By N. Euler, M. Euler. 2004

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Abstract We investigate the Sundman symmetries of second-order and third-order nonlinear ordinary differential equations. These symmetries, which are in general nonlocal transformations, arise from generalised Sundman transformations of autonomous equations. We show that these transformations and symmetries can be calculated systematically and can be used to find first integrals of the equations.

Subfields: Spectroscopy, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/db0d6b02ce22e4ffe3612b4a7d30caccbe5d9b27