A KAM theorem with applications to partial differential equations of higher dimensions

被引：23

作者：

Yuan, Xiaoping ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Fudan Univ, Key Lab Math Nonliner Sci, Shanghai 200433, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2007年 / 275卷 / 01期

关键词：

D O I：

10.1007/s00220-007-0287-2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The existence of lower dimensional KAM tori is shown for a class of nearly integrable Hamiltonian systems of infinite dimensions where the second Melnikov's conditions are completely eliminated and the algebraic structure of the normal frequencies are not needed. As a consequence, it is proved that there exist many invariant tori and thus quasi-periodic solutions for nonlinear wave equations, Schrodinger equations and other equations of any spatial dimensions.

引用

页码：97 / 137

页数：41

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