Jianjun Liu, Xiaoping Yuan
A KAM Theorem for Hamiltonian Partial Differential Equations with Unbounded Perturbations
(447K, .pdf)

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 $\partial_x$ in the perturbation. Especially, in this range of application lie a class of derivative nonlinear Schrodinger 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.