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A KAM Theorem with Applications to Partial Differential Equations of Higher Dimensions

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An Erratum to this article was published on 21 June 2011

Abstract

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, Schrödinger equations and other equations of any spatial dimensions.

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Authors and Affiliations

  1. School of Mathematical Sciences and Key Lab of Mathematics for Nonlinear Science, Fudan University, Shanghai, 200433, China

    Xiaoping Yuan

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  1. Xiaoping Yuan
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Correspondence to Xiaoping Yuan.

Additional information

Communicated by G. Gallavotti.

Supported by NNSFC and NCET-04-0365 and STCSM-06ZR14014.

An erratum to this article is available at http://dx.doi.org/10.1007/s00220-011-1283-0.

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Yuan, X. A KAM Theorem with Applications to Partial Differential Equations of Higher Dimensions. Commun. Math. Phys. 275, 97–137 (2007). https://doi.org/10.1007/s00220-007-0287-2

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  • DOI: https://doi.org/10.1007/s00220-007-0287-2

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