Abstract
We consider the integrability property of coupled polynomial nonlinear oscillators from the point of view of symmetries, with two degrees of freedom as a prototype example. It is shown how invariance of the equations of motion under generalised Lie transformations can lead to the identification of integrable cases. The perturbed Kepler problem is treated explicitly. Results on other two-dimensional systems are presented briefly.
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© 1990 Springer-Verlag Berlin Heidelberg
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Senthilvelan, M., Lakshmanan, M. (1990). Generalised Lie Symmetries and Integrability of Coupled Nonlinear Oscillators with Two Degrees of Freedom. In: Lakshmanan, M., Daniel, M. (eds) Symmetries and Singularity Structures. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76046-4_7
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DOI: https://doi.org/10.1007/978-3-642-76046-4_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53092-3
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