Spectral stability of multi-pulses via the Krein matrix


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.

Apr 17, 2019
IMACS Conference on Nonlinear Evolution Equations and Wave Phenomena
Athens, GA
Ross Parker
Ross Parker
RTG postdoctoral fellow

I am a postdoctoral fellow in the department of mathematics at Southern Methodist University.