A KAM Theorem for Hamiltonian Partial Differential Equations in Higher Dimensional Spaces
A KAM Theorem for Hamiltonian Partial Differential Equations in Higher Dimensional Spaces
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DOI：
10.1007/s00220-005-1497-0
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发表时间：
2006-03
影响因子：
2.4
通讯作者：
J. Geng;J. You
中科院分区：
文献类型：
--
作者：
J. Geng;J. You
本文给出了一类无穷维近可积Hamilton系统的KAM定理。该定理可应用于高维空间中某些具有周期边界条件的Hamilton偏微分方程，构造线性稳定的拟周期解及其局部Birkhoff标准形.文中还给出了该方法在高维梁方程和具有非局部光滑非线性项的高维薛定谔方程中的应用。
In this paper, we give a KAM theorem for a class of infinite dimensional nearly integrable Hamiltonian systems. The theorem can be applied to some Hamiltonian partial differential equations in higher dimensional spaces with periodic boundary conditions to construct linearly stable quasi–periodic solutions and its local Birkhoff normal form. The applications to the higher dimensional beam equations and the higher dimensional Schrödinger equations with nonlocal smooth nonlinearity are also given in this paper.