64 citations · 378 across the 32 of their papers we have counts for
43 papers
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…
Modulational Instability in the Ostrovsky Equation and Related Models
Bhavna, Mathew A. Johnson, Ashish Kumar Pandey
We study the modulational instability of small-amplitude periodic traveling wave solutions in a dispersion generalized Ostrovsky equation. Specifically, we investigate the invertib…
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…
Solitary waves in a Whitham equation with small surface tension
Mathew A. Johnson, Tien Truong, Miles H. Wheeler
Using a nonlocal version of the center manifold theorem and a normal form reduction, we prove the existence of small-amplitude generalized solitary-wave solutions and modulated sol…