5 papers · 1 filter
Convergence of linear solutions through convergence of periodic initial data
Harrison Gaebler, Wesley R Perkins
When studying the stability of -periodic solutions to partial differential equations, it is common to encounter subharmonic perturbations, i.e. perturbations which have a period…
On the Modulation of Wave Trains in the Ostrovsky Equation
Mathew A. Johnson, Jeffrey Oregero, Wesley R. Perkins
We consider the nonlinear wave modulation of arbitrary amplitude periodic traveling wave solutions of the Ostrovsky equation, which arises as a model for the unidirectional propaga…
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…
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…
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…