43 citations · 108 across the 3 of their papers we have counts for
4 papers
Spectral Stability of Inviscid Roll Waves
Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues +2
We carry out a systematic analytical and numerical study of spectral stability of discontinuous roll wave solutions of the inviscid Saint Venant equations, based on a periodic Evan…
Modulational Instability in the Whitham Equation for Water Waves
Vera Mikyoung Hur, Mathew A. Johnson
We show that periodic traveling waves with sufficiently small amplitudes of the Whitham equation, which incorporates the dispersion relation of surface water waves and the nonlinea…
Nonlocalized modulation of periodic reaction diffusion waves: Nonlinear stability
Mathew Johnson, Pascal Noble, L. Miguel Rodrigues +1
By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stabili…
Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation
Mathew Johnson, Pascal Noble, L. Miguel Rodrigues +1
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems…