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It is proved that the KAM tori (thus quasi-periodic solutions) are long timestable for infinite dimensional Hamiltonian systems generated by nonlinear waveequation, by constructing a partial normal form of higher order around the KAMtorus and showing $p$-tame property persists under KAM iterative procedure andnormal form iterative procedure.

Long time stability of KAM tori for nonlinear wave equation