A KAM theorem with applications to partial equations of higher dimension
  The existence of lower dimensional KAM tori is shown for a class of nearly integrable Hamiltonian systems where the second Melnikov's conditions are eliminated. As a consequence, it is proved that there exist many invariant tori and thus quasi-periodic solutions for nonlinear wave equations, Schr\"odinger equations and other equations of higher spatial dimension. 
Xiaoping Yuan