Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups
Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups
复制标题
具有部分李对称群的渐近动力系统的推导
DOI：
10.1155/2015/601657
复制
发表时间：
2015
影响因子：
--
通讯作者：
M. Iwasa
中科院分区：
文献类型：
--
作者：
M. Iwasa
李群分析已被应用到奇异摄动问题的常微分方程和差分方程，并允许我们找到减少动力学描述的渐近行为的动力系统。本研究提供了一个扩展的方法，也适用于偏微分方程。扩展方法的主要特点是通过一些约束方程对流形进行限制，在这些约束方程上我们寻找一个李对称群。这种扩展使得有可能找到一个部分李对称群，这导致了一个减少的动力学描述的渐近行为。
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.