3 papers
math.CA2023
Floquet theory and stability for Hamiltonian partial differential equations
Jared C Bronski, Vera Mikyoung Hur, Robert Marangell
We analyze Floquet theory as it applies to the stability and instability of periodic traveling waves in Hamiltonian PDEs. Our investigation focuses on several examples of such PDEs…
math.DS2023
A geometric singular perturbation analysis of generalised shock selection rules in reaction-nonlinear diffusion models
Bronwyn H Bradshaw-Hajek, Ian Lizarraga, Robert Marangell +1
Reaction-nonlinear diffusion (RND) partial differential equations are a fruitful playground to model the formation of sharp travelling fronts, a fundamental pattern in nature. In t…
math.AP2014
Dynamical Hamiltonian-Hopf instabilities of periodic traveling waves in Klein-Gordon equations
Robert Marangell, Peter D. Miller
We study the unstable spectrum close to the imaginary axis for the linearization of the nonlinear Klein-Gordon equation about a periodic traveling wave in a co-moving frame. We def…