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Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems.

Kapitula, T., Kevrekidis, P. G. and Sandstede, B. (2004) Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems. Physica D, 195 (2004). pp. 263-282.

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Abstract

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.

Item Type: Article
Additional Information: Physica D 195 (2004) 263-282.
Uncontrolled Keywords: Krein signature, Nonlinear, Hamiltonian
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1516

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