Symmetries of nonlinear ordinary differential equations: The modified Emden equation as a case study

摘要

Lie symmetry analysis is one of the powerful tools to analyse nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries, contact symmetries, hidden symmetries, nonlocal symmetries, e???-symmetries, adjoint symmetries and telescopic vector fields of a secondorder ordinary differential equation. We also illustrate the algorithm involved in each method by considering a nonlinear oscillator equation as an example. The connections betweensymmetries and integrating factors and