Reduction of dynamics with Lie group analysis (Q447499)

Summary: This paper is mainly a review concerning singular perturbation methods by means of Lie group analysis which have been presented by the author earlier. We make use of a particular type of approximate Lie symmetries in those methods in order to construct reduced systems which describe the long-time behavior of the original dynamical system. Those methods can be used in analyzing not only ordinary differential equations but also difference equations. Although this method has been mainly used in order to derive the asymptotic behavior, when we can find exact Lie symmetries, we succeed in constructing exact solutions.