3 papers
math.AP2021
Subharmonic Dynamics of Wave Trains in the Korteweg-de Vries / Kuramoto-Sivashinsky Equation
Mathew A. Johnson, Wesley R. Perkins
We study the stability and nonlinear local dynamics of spectrally stable periodic wave trains of the Korteweg-de Vries / Kuramoto-Sivashinsky equation when subjected to classes of…
math.AP2020
Linear Modulational and Subharmonic Dynamics of Spectrally Stable Lugiato-Lefever Periodic Waves
Mariana Haragus, Mathew A. Johnson, Wesley R. Perkins
We study the linear dynamics of spectrally stable -periodic stationary solutions of the Lugiato-Lefever equation (LLE), a damped nonlinear Schrödinger equation with forcing that…
math.AP2019
Modulational Instability of Viscous Fluid Conduit Periodic Waves
Mathew A. Johnson, Wesley R. Perkins
In this paper, we are interested in studying the modulational dynamics of interfacial waves rising buoyantly along a conduit of a viscous liquid. Formally, the behavior of modulate…