Renormalization Group and the Melnikov Problem for PDE's

Details Renormalization Group and the Melnikov Problem for PDE's Renormalization Group and the Melnikov Problem for PDE's

2001-02-28

arxiv.org/abs/math-ph/0102036v1

Physics

Mathematical Physics

44 pages, plain TeX

Scientific paper

10.1007/s002200100471

We give a new proof of persistence of quasi-periodic, low dimensional elliptic tori in infinite dimensional systems. The proof is based on a renormalization group iteration that was developed recently in [BGK] to address the standard KAM problem, namely, persistence of invariant tori of maximal dimension in finite dimensional, near integrable systems. Our result covers situations in which the so called normal frequencies are multiple. In particular, it provides a new proof of the existence of small-amplitude, quasi-periodic solutions of nonlinear wave equations with periodic boundary conditions.

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