Invariant characterization of scalar third-order ODEs that admit the maximal contact symmetry Lie algebra

Abstract

The Cartan equivalence method is utilized to deduce an invariant characterization of the scalar third-order ordinary differential equation $u^{\prime \prime \prime }=f(x,u,u^{\prime },u^{\prime \prime })$ which admits the maximal ten-dimensional contact symmetry Lie algebra. The method provides auxiliary functions which can be used to efficiently determine the contact transformation that does the reduction to the simplest linear equation ${\bar{u}}^{\prime \prime \prime }=0$. Furthermore, ample examples are given to illustrate our method.

arXiv admin note: text overlap with arXiv:1712.02387