64 citations · 378 across the 32 of their papers we have counts for
5 papers · 2 filters
Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations
Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues +1
We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asympt…
Stability of Small Periodic Waves in Fractional KdV Type Equations
Mathew A. Johnson
We consider the effects of varying dispersion and nonlinearity on the stability of periodic traveling wave solutions of nonlinear PDE of KdV-type, including generalized KdV and Ben…
An Instability Index Theory for Quadratic Pencils and Applications
Jared Bronski, Mathew A. Johnson, Todd Kapitula
Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic ope…
Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation
Blake Barker, Mathew A. Johnson, Pascal Noble +2
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the lo…
Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit
Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues +1
We study the spectral stability of a family of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation $ \partial_t v+v\partial_x v+\partial_x^3 v+δ(\partial_x^…