Four lectures on KAM for the non-linear Schrodinger equation

被引：3
|
作者：
Eliasson, L. H. [1 ]
Kuksin, S. B. [2 ]
机构：
[1] Univ Paris 07, Dept Math, Paris, France
[2] Heriot Watt Univ, Dept Math, Edinburgh, Midlothian, Scotland
来源：
HAMILTONIAN DYNAMICAL SYSTEMS AND APPLICATIONS | 2008年
关键词：
D O I：
10.1007/978-1-4020-6964-2_10
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We discuss the KAM-theory for lower-dimensional ton for the non-linear Schrodinger equation with periodic boundary conditions and a convolution potential in dimension d. Central in this theory is the homological equation and a condition on the small divisors often known as the second Melnikov condition. The difficulties related to this condition are substantial when d >= 2. We discuss this difficulty, and we show that a block decomposition and a Toplitz-Lipschitz-property, present for non-linear Schrodinger equation, permit to overcome this difficuly. A detailed proof is given in [EK06].
引用
收藏
页码：179 / +
页数：2
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