Long time stability of KAM tori for nonlinear wave equation
  It is proved that the KAM tori (thus quasi-periodic solutions) are long time stable for infinite dimensional Hamiltonian systems generated by nonlinear wave equation, by constructing a partial normal form of higher order around the KAM torus and showing $p$-tame property persists under KAM iterative procedure and normal form iterative procedure. 
Cong Hongzi, Gao Meina and Liu Jianjun
math.DS