Inequivalence of Classes of Linearizable Systems of Second Order Ordinary Differential Equations Obtained by Real and Complex Symmetry Analysis

Linearizability criteria for systems of two cubically semi-linear second order ordinary differential equations (ODEs) were obtained by geometric means using real symmetry analysis (RSA). Separately, complex symmetry analysis (CSA) was developed to provide means to discuss systems of two ODEs. It was shown that CSA provides a class of linearizable systems of two cubically semi-linear ODEs. Linearizability criteria for this class were also developed. It is proved that the two classes of linearizable systems of two ODEs, provided by CSA and RSA, are inequivalent under point transformations.