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

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  • M. Safdar
  • Asghar Qadir
  • S. Ali

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.

Suggested Citation

  • M. Safdar & Asghar Qadir & S. Ali, 2011. "Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-17, October.
    • Handle: RePEc:hin:jnlmpe:171834
    DOI: 10.1155/2011/171834
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