On the spectra of periodic waves for infinite-dimensional Hamiltonian systems

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Instability, index theorem, and exponential trichotomy for Linear Hamiltonian PDEs (2017, methodology): “33) was proved in [32] for the case when kerLk = {0}, with additional assumptions to ensure that the generalized eigenfunctions of JkLk form a complete basis of L (S) as assumed in the case of co-periodic perturbations.”
An Instability Index Theory for Quadratic Pencils and Applications (2012, background): “, see [18,25,26,32] and the references therein), and for this problem it has firmly been established that the intuition is indeed correct.”
The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation (2011, methodology): “Let us consider the implications of this theorem for the problem at hand: • An application of the SCS basis lemma in [6] establishes that the eigenfunctions W form a basis for Lper([−NT,NT ]), for any integer N , when the potential U is periodic in y with period 2T .”