In this paper, we prove an infinite dimensional Kolmogorov-Arnold-Moser theorem. As an application, it is shown that there are many small-amplitude linearly-stable quasi-periodic solutions for higher dimensional wave equations with a real Fourier multiplier, which are under nonlocal and forced perturbations with a special structure in space and short range property.

中文翻译：

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非局部和强制扰动下高维波动方程的可约 KAM 环

在本文中，我们证明了一个无限维 Kolmogorov-Arnold-Moser 定理。作为一个应用，证明了具有实傅立叶乘子的高维波动方程有许多小幅度线性稳定准周期解，这些方程在非局域和强迫扰动下具有特殊的空间结构和短程性质。