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DCDS

In this note, it is shown that some Hamiltonian partial
differential equations such as semi-linear Schrödinger
equations, semi-linear wave equations and semi-linear beam
equations are partially integrable, i.e., they possess integrable
invariant manifolds foliated by invariant tori which carry
periodic or quasi-periodic solutions. The linear stability of the
obtained invariant manifolds is also concluded. The proofs are
based on a special invariant property of the considered equations
and a symplectic change of variables first observed in [26].

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