Stéphane Lafortune University of Arizona and School of Mathematics, University of Sydney Stability analysis of local deformations of an elastic rod Wednesday 26th, May 14:05-14:55pm, Carslaw Building Room 359. It is often possible to use the Hamiltonian structure of a system of partial differential equations for studying the stability of localized structures such as pulses and fronts. I will present a work in which this is done for pulse solutions to two coupled nonlinear Klein-Gordon equations (CNLKG). These equations describe the near-threshold dynamics of an elastic rod with circular cross-section. Furthermore, if time permits, I will show how the numerical computation of the Evans function is used to obtain information on the spectrum of the linearisation of the CNLKG about the pulse solutions.