Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups

Lie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. This extension makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics describing the asymptotic behavior.