7 citations · 15 across the 8 of their papers we have counts for
10 papers
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…
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 wit…
Rigorous justification of the Whitham modulation equations for equations of Whitham-type
William A. Clarke, Robert Marangell, Wesley R. Perkins
We prove that the modulational instability criterion of the formal Whitham modulation theory agrees with the spectral stability of long wavelength perturbations of periodic travell…
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…
Nonlinear Modulational Dynamics of Spectrally Stable Lugiato-Lefever Periodic Waves
Mariana Haragus, Mathew A. Johnson, Wesley R. Perkins +1
We consider the nonlinear stability of spectrally stable periodic waves in the Lugiato-Lefever equation (LLE), a damped nonlinear Schrödinger equation with forcing that arises in n…
Moving modulating pulse and front solutions of permanent form in a FPU model with nearest and next-to-nearest neighbor interaction
Bastian Hilder, Björn de Rijk, Guido Schneider
We consider a nonlinear chain of coupled oscillators, which is a direct generalization of the classical FPU lattice and exhibits, besides the usual nearest neighbor interaction, al…
Subharmonic Dynamics of Wave Trains in Reaction Diffusion Systems
Mathew A. Johnson, Wesley R. Perkins
We investigate the stability and nonlinear local dynamics of spectrally stable wave trains in reaction-diffusion systems. For each , such -periodic traveling wav…
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…