On linear stability of KAM tori via the Craig-Wayne-Bourgain method

具有无界扰动的多维非线性波动方程周期解的构造

Construction of periodic solutions of multi-dimensional nonlinear wave equations with unbounded perturbation

本文应用Craig-Wayne-Bourgain (CWB)方法，证明了具有无界扰动的多维非线性波动方程(NLW)周期解的持久性。

Construction of quasi-periodic solutions for delayed perturbation differential equations

We employ the Craig-Wayne-Bourgain method to construct quasi-periodic solutions for delayed perturbation differential equations. Our results not only implement the existing literatures on constructing quasi-periodic solutions for DDE by the KAM method and space splitting technique, but also provide an example of application of multi-scale analysis method to non-selfadjoint problem.

Almost-periodic Response Solutions for a forced quasi-linear Airy equation

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 ${\mathbb T}^\infty$.