We prove the existence of almost-periodic solutions for quasi-linear perturbations of the Airy equation. This is the first result about the existence of this type of solutions for a quasi-linear PDE. The solutions turn out to be analytic in time and space. To prove our result we use a Craig–Wayne approach combined with a KAM reducibility scheme and pseudo-differential calculus on \(\mathbb {T}^\infty \).

中文翻译：

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强迫拟线性Airy方程的概周期响应解

我们证明了Airy方程的拟线性扰动的概周期解的存在。这是关于准线性PDE这类解决方案的存在的第一个结果。事实证明，这些解决方案在时间和空间上都是分析性的。为了证明我们的结果，我们使用了Craig–Wayne方法，并结合了\（\ mathbb {T} ^ \ infty \）上的KAM可约性方案和伪微积分。