A KAM Theorem for Hamiltonian Partial Differential Equations in Higher Dimensional Spaces

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KAM for the nonlinear beam equation (2016, background): “A result for the beam equation (which is a simpler model than the Schrödinger and wave equations) was first obtained in [19] and [20].”
A KAM algorithm for the resonant non-linear Schrödinger equation (2012, background): “KAM results for PDEs in dimension d > 1 are few and relatively recent, see for instance [11], and in particular the paper [8] which studies an NLS with external parameters.”
KAM for Reversible Derivative Wave Equations (2012, methodology): “This is an important novelty with respect to the KAM theorem in [4] which used the conservation of momentum, as [17], [18].”
An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation (2011, background): “You, KAM tori for 1D nonlinear wave equations with periodic boundary conditions, Comm. Math.”