High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs
High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs
Generalizing ideas of MacKay, and MacKay and Saffman, a necessary condition for the presence of high-frequency (i.e., not modulational) instabilities of small-amplitude periodic solutions of Hamiltonian partial differential equations is presented, entirely in terms of the Hamiltonian of the linearized problem. With the exception of a Krein signature calculation, the …