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Journal of Applied Mathematics
Volume 2015, Article ID 601657, 8 pages
http://dx.doi.org/10.1155/2015/601657
Research Article

Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups

General Education Department, Aichi Institute of Technology, 1247 Yachigusa Yakusacho, Toyota 470-0392, Japan

Received 16 July 2015; Revised 12 September 2015; Accepted 14 September 2015

Academic Editor: Wan-Tong Li

Copyright © 2015 Masatomo Iwasa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.