Abstract
Hamiltonian methods are used to obtain a necessary and sufficient condition for the spectral stability of pulse solutions to two coupled nonlinear Klein--Gordon equations. These equations describe the near-threshold dynamics of an elastic rod with circular cross section. The present work completes and extends a recent analysis of the authors' [Phys. D, 182 (2003), pp. 103--124], in which a sufficient condition for the instability of "nonrotating" pulses was found by means of Evans function techniques.
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