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

• Main Authors: M. Safdar, Asghar Qadir, S. Ali
• Format: Article
• Language: English
• Published: Hindawi Limited 2011-01-01
• Series: Mathematical Problems in Engineering
• Online Access: http://dx.doi.org/10.1155/2011/171834

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.