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arXiv · 1104.3198

Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis

Muhammad Safdar·Asghar Qadir·Sajid Ali
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Abstract

Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables. An "optimal (or simplest) canonical form" of linear systems had been established to obtain the symmetry structure, namely with 5, 6, 7, 8 and 15 dimensional Lie algebras. For those systems that arise from a scalar complex second-order ordinary differential equation, treated as a pair of real ordinary differential equations, a "reduced optimal canonical form" is obtained. This form yields three of the five equivalence classes of linearizable systems of two dimensions. We show that there exist 6, 7 and 15-dimensional algebras for these systems and illustrate our results with examples.

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Muhammad Safdar, Asghar Qadir, Sajid Ali. 2011-04-16. Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis. https://arxiv.org/abs/1104.3198

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