Approximation of solutions of the cubic nonlinear Schrödinger equations by finite-dimensional equations and nonsqueezing properties
Approximation of solutions of the cubic nonlinear Schrödinger equations by finite-dimensional equations and nonsqueezing properties
复制标题
用有限维方程和非挤压性质逼近三次非线性薛定谔方程的解
DOI：
--
复制
发表时间：
1994
期刊：
影响因子：
--
通讯作者：
J. Bourgain
中科院分区：
文献类型：
--
作者：
J. Bourgain
我们证明了某些非线性薛定谔方程的非挤压结果，将 S. Kuksin [Kuk] 最近的一些工作扩展到 NLSE。这种情况的主要特征是流图不是辛希尔伯特空间中线性图的紧扰动。该方法包括将问题直接简化为有限维模型，其中辛容量保持成立。这是通过详细阐述 [Bo1]、[Bo2] 的一些技术来实现的。非线性的精确形式在此论证中非常重要。
We prove a nonsqueezing result for certain nonlinear Schrödinger equations, extending to the NLSE some recent work of S. Kuksin [Kuk]. The main feature of this situation is that the flow map is not a compact perturbation of a linear map in the symplectic Hilbert space. The method consists of a direct reduction of the problem to a finite-dimensional model where the symplectic capacity preservation holds. This is achieved by elaborating some of the techniques of [Bo1], [Bo2]. The precise form of the nonlinearity is of importance in this argument.