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KAM theory with applications to Hamiltonian partial differential equations

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Hamiltonian Dynamical Systems and Applications

Part of the book series: NATO Science for Peace and Security Series ((NAPSB))

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In these notes I present a KAM theorem on the existence of lower dimensional invariant tori 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 is not required. This theorem can be used to construct invariant tori and 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, Fudan University, 200433, Shanghai, China

    Xiaoping Yuan

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  1. Xiaoping Yuan
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Editors and Affiliations

  1. McMaster University, L8S 4K1, Hamilton, ON, Canada

    Walter Craig

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Yuan, X. (2008). KAM theory with applications to Hamiltonian partial differential equations. In: Craig, W. (eds) Hamiltonian Dynamical Systems and Applications. NATO Science for Peace and Security Series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6964-2_9

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