标题： 重正化群与偏微分方程的梅尔尼科夫问题 显示英文标题

标题： Renormalization Group and the Melnikov Problem for PDE's

摘要： 我们给出了无限维系统中拟周期、低维椭圆环面持久性的新证明。 该证明基于一种重正化群迭代方法，该方法最近在[BGK]中被发展用于解决标准KAM问题，即有限维近可积系统的最大维数不变环面的持久性。 我们的结果涵盖了所谓的法向频率是多重的情况。 特别地，它为具有周期边值条件的非线性波动方程的小振幅拟周期解的存在性提供了新的证明。 显示英文摘要

摘要： 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.