论文标题
准周期强制NLS的可降低性和非线性稳定性
Reducibility and nonlinear stability for a quasi-periodically forced NLS
论文作者
论文摘要
由长时间稳定性问题与非线性立方体schrödinger方程（NLS）的不稳定性的问题所激发的动机，在两个维圆环$ \ mathbb t^2：=（\ Mathbb r/2π\ Mathbb z）^2 $中在kam torus。我们证明了可降低的结果以及原点的长时间稳定性。主要的新颖性是获得频率的精确渐近扩展，这使我们能够以任意顺序强加墨尼科夫条件。
Motivated by the problem of long time stability vs. instability of KAM tori of the Nonlinear cubic Schrödinger equation (NLS) on the two dimensional torus $\mathbb T^2:= (\mathbb R/2π\mathbb Z)^2$, we consider a quasi-periodically forced NLS equation on $\mathbb T^2$ arising from the linearization of the NLS at a KAM torus. We prove a reducibility result as well as long time stability of the origin. The main novelty is to obtain the precise asymptotic expansion of the frequencies which allows us to impose Melnikov conditions at arbitrary order.
