A KAM Theorem for Hamiltonian Partial Differential Equations with Unbounded Perturbations


DOI: 10.1007/s00220-011-1353-3

Cite this article as:
Liu, J. & Yuan, X. Commun. Math. Phys. (2011) 307: 629. doi:10.1007/s00220-011-1353-3


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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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Mathematical Sciences and Key Lab of Math. for Nonlinear ScienceFudan UniversityShanghaiP.R. China

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