Spectral stability of multi-pulses via the Krein matrix

Abstract

The Chen-Mckenna suspension bridge equation is a nonlinear PDE which is 2nd order in time and is used to model traveling waves on a suspended beam. For certain parameter regimes, it admits multi-pulse traveling wave solutions, which are small perturbations of the stable, primary pulse solution. Linear stability of these multi-pulse solutions is determined by eigenvalues near the origin representing the interaction between the individual pulses. Linearization about these multi-pulse solutions yields a quadratic eigenvalue problem. To study this problem, we use a reformulated version of the Krein matrix, which was presented by Todd Kapitula in a previous talk. Using an appropriate leading order expansion of the Krein matrix, we are able to give analytical criteria for the stability of these multi-pulse solutions. We also present numerical results to support our analysis.

Date
Apr 17, 2019
Location
Athens, GA
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Ross Parker
Ph.D. Student in Applied Mathematics

I am a sixth-year Ph.D. student in the Division of Applied Mathematics at Brown University interested in nonlinear waves and dynamical systems.