A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation
A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation
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DOI：
10.4171/rlm/873
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发表时间：
2019-01-01
影响因子：
0.5
通讯作者：
Procesi, Michela
中科院分区：
文献类型：
--
作者：
Guardia, Marcel;Hani, Zaher;Procesi, Michela
我们给出了[29]中关于二维环面上散焦立方非线性Schrodinger方程（NLS）的强非线性不稳定性和Sobolev范数在拟周期有限间隙解附近的增长性的最新结果.该方程承认一个特殊的家庭椭圆不变的准周期环面称为有限间隙的解决方案。这些都是继承自可积的一维模型（立方NLS的圆圈），考虑解决方案，只依赖于一个变量。我们构造了二维三次NLS的解，这些解在H-s拓扑（0 < s < 1）中任意接近这样的不变环面，并且其H-s范数可以以任何给定的因子增长。
We present the recent result in [29] concerning strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap solutions of the defocusing cubic nonlinear Schrodinger equation (NLS) on the two-dimensional torus. The equation admits a special family of elliptic invariant quasiperiodic tori called finite-gap solutions. These are inherited from the integrable 1D model (cubic NLS on the circle) by considering solutions that depend only on one variable. We construct solutions of the 2D cubic NLS that start arbitrarily close to such invariant tori in the H-s topology (0 < s < 1) and whose H-s norm can grow by any given factor.