五次NLS拍解的KAM
KAM for beating solutions of the quintic NLS
摘要：
考虑圆$\mathbb{S}^1 = \mathbb{R}/2π$上的五次非线性薛定谔方程.我们证明了拟周期解的存在性，这些解是从[14]中所研究的系统的“共振”解分叉出来的，这些解是在Birkhoff标准形的一步之后截断Hamilton而得到的，表现出某些Fourier模式之间的循环能量交换。这些拟周期解的存在性是一个纯粹的非线性效应。
英文摘要：
We consider the nonlinear Schrödinger equation of degree five on the circle $\mathbb{S}^1 = \mathbb{R}/2π$. We prove the existence of quasi-periodic solutions which bifurcate from "resonant" solutions (studied in [14]) of the system obtained by truncating the Hamiltonian after one step of Birkhoff normal form, exhibiting recurrent exchange of energy between some Fourier modes. The existence of these quasi-periodic solutions is a purely nonlinear effect.
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