Solution of reduced equations derived with singular perturbation methods

Details Solution of reduced equations derived with singular perturbation methods Solution of reduced equations derived with singular perturbation methods

2008-11-24

arxiv.org/abs/0811.3803v1

Nonlinear Sciences

Chaotic Dynamics

To be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.78.066213

For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the normal form method, center manifold theory, the renormalization group method are well known. In this paper, it is shown that all of the solutions of the reduced equations constructed with those methods are exactly equal to sum of the most divergent secular terms appearing in the naive expansion. For the proof, a method to construct a perturbation solution which differs from the conventional one is presented, where we make use of the theory of Lie symmetry group.

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