A KAM Theorem for Hamiltonian Partial Differential Equations with Unbounded Perturbations

被引：0

作者：

Jianjun Liu

Xiaoping Yuan

机构：

[1] Fudan University,School of Mathematical Sciences and Key Lab of Math. for Nonlinear Science

来源：

Communications in Mathematical Physics | 2011年 / 307卷

关键词：

Normal Form; Hamiltonian Vector; Homological Equation; Birkhoff Normal Form; Hamiltonian PDEs;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We establish an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field, which could be applied to a large class of Hamiltonian PDEs containing the derivative ∂x in the perturbation. Especially, in this range of application lie a class of derivative nonlinear Schrödinger equations with Dirichlet boundary conditions and perturbed Benjamin-Ono equation with periodic boundary conditions, so KAM tori and thus quasi-periodic solutions are obtained for them.

引用

页码：629 / 673

页数：44

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