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math.AP2025
Asymptotic stability of sharp fronts: Analysis and rigorous computation
Blake Barker, Jared C. Bronski, Vera Mikyoung Hur +1
We investigate the stability of traveling front solutions to nonlinear diffusive-dispersive equations of Burgers type, with a primary focus on the Korteweg-de Vries-Burgers (KdVB)…
math.AP2024
Bounds on unstable spectrum for dispersive Hamiltonian PDEs
Jared C Bronski, Ver Mikyoung Hur, Sarah E Simpson
We study quasi-periodic eigenvalue problems that arise in the stability analysis of periodic traveling wave solutions to Hamiltonian PDEs. We establish bounds on regions in the com…