Article

Communications in Mathematical Physics

, 307:629

First online:

A KAM Theorem for Hamiltonian Partial Differential Equations with Unbounded Perturbations

  • Jianjun LiuAffiliated withSchool of Mathematical Sciences and Key Lab of Math. for Nonlinear Science, Fudan University
  • , Xiaoping YuanAffiliated withSchool of Mathematical Sciences and Key Lab of Math. for Nonlinear Science, Fudan University Email author 

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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.