4 papers
Long-time behavior of small solutions in the viscoelastic Klein-Gordon equation
Louis Garénaux, Björn de Rijk
We investigate the long-time behavior of solutions with small initial data to the viscoelastic Klein-Gordon equation with general smooth nonlinearity. Our analysis relies on the sp…
Multiple front and pulse solutions in spatially periodic systems
Lukas Bengel, Björn de Rijk
In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semi…
Nonlinear stability and asymptotic behavior of periodic wave trains in reaction-diffusion systems against -perturbations
Björn de Rijk
We present a nonlinear stability theory for periodic wave trains in reaction-diffusion systems, which relies on pure -estimates only. Our analysis shows that localization…
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…