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A KAM Theorem for Hamiltonian Partial Differential Equations with Unbounded Perturbations

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Abstract

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.

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Authors and Affiliations

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

    Jianjun Liu & Xiaoping Yuan

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  1. Jianjun Liu
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  2. Xiaoping Yuan
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Correspondence to Xiaoping Yuan.

Additional information

Communicated by G. Gallavotti

Supported by NNSFC, 973 Program (No. 2010CB327900), the Research Foundation for Doctor Programme, China Postdoctoral Science Foundation (No. 20100480553), China Postdoctoral Special Science Foundation (No. 201104236), Shanghai Postdoctoral Science Foundation (No. 11R21412000).

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Liu, J., Yuan, X. A KAM Theorem for Hamiltonian Partial Differential Equations with Unbounded Perturbations. Commun. Math. Phys. 307, 629–673 (2011). https://doi.org/10.1007/s00220-011-1353-3

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  • DOI: https://doi.org/10.1007/s00220-011-1353-3

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