A Semi-Algorithmic Search for Lie Symmetries

Details A Semi-Algorithmic Search for Lie Symmetries A Semi-Algorithmic Search for Lie Symmetries

2010-07-16

arxiv.org/abs/1007.2861v1

Physics

Mathematical Physics

Scientific paper

In [Solving second order ordinary differential equations by extending the Prelle-Singer method, J. Phys. A: Math.Gen., 34, 3015-3024 (2001)] we defined a function (we called S) associated to a rational second order ordinary differential equation (rational 2ODE) that is linked to the search of an integrating factor. In this work we investigate the relation between these $S$-functions and the Lie symmetries of a rational 2ODE. Based on this relation we can construct a semi-algorithmic method to find the Lie symmetries of a 2ODE even in the case where it presents no Lie point symmetries.

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