DCDS
The existence of integrable invariant manifolds of Hamiltonian partial differential equations
Rongmei Cao Jiangong You
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].
keywords: Integrability Hamiltonian PDEs KAM theorem.

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