Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
نویسندگان
چکیده
Spectra of nonlinear waves in infinite-dimensional Hamiltonian systems are investigated. We establish a connection via the Krein signature between the number of negative directions of the second variation of the energy and the number of potentially unstable eigenvalues of the linearization about a nonlinear wave. We apply our results to determine the effect of symmetry-breaking on the spectral stability of nonlinear waves in weakly coupled nonlinear Schrödinger equations. ∗E-mail: [email protected] †E-mail: [email protected] ‡E-mail: [email protected]
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