64 citations · 378 across the 32 of their papers we have counts for
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Note on the stability of viscous roll-waves
Blake Barker, Mathew A. Johnson, Pascal Noble +2
In this note, we announce a complete classification of stability of periodic roll-wave solutions of the viscous shallow-water equations, from their onset at Froude number $F\approx…
Modulational Instability in the Whitham Equation with Surface Tension and Vorticity
Vera Mikyoung Hur, Mathew A. Johnson
We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and mod…
Stability of viscous St. Venant roll-waves: from onset to infinite-Froude number limit
Blake Barker, Mathew A. Johnson, Pascal Noble +2
We study the spectral stability of roll-wave solutions of the viscous St. Venant equations modeling inclined shallow-water flow, both at onset in the small-Froude number or "weakly…
Modulational Instability in Equations of KdV Type
Jared C. Bronski, Vera Mikyoung Hur, Mathew A. Johnson
It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their charact…