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

M. Safdar, Asghar Qadir and S. Ali

Mathematical Problems in Engineering, 2011, vol. 2011, 1-17

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, we provide a “reduced optimal canonical form.†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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:171834

DOI: 10.1155/2011/171834

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