An alternative proof of Lie's linearization theorem using a new lambda-symmetry criterion

摘要

An alternative proof of Lie's approach for the linearization of scalar second-order ordinary differential equations is derived by using the relationship between lambda-symmetries and first integrals. This relation further leads to a new lambda-symmetry linearization criterion for second- order ordinary differential equations which provides a new approach for constructing the linearization transformations with lower complexity. The effectiveness of the approach is illustrated by obtaining the local linearization transformations for the linearizable nonlinear ordinary differential equations of the form y '' + F-1(x,y)y' + F(x,y) = 0. Examples of linearizable nonlinear ordinary differential equations which are quadratic or cubic in the first derivative are also presented. (C) 2015 Elsevier B.V. All rights reserved.