3 papers
math.AP2025
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…
math.AP2025
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…
math.AP2024
Nonlinear Subharmonic Dynamics of Spectrally Stable Lugiato-Lefever Periodic Waves
Mariana Haragus, Mathew A. Johnson, Wesley R. Perkins +1
We study the nonlinear dynamics of perturbed, spectrally stable -periodic stationary solutions of the Lugiato-Lefever equation (LLE), a damped nonlinear Schrödinger equation wi…