4 papers · 1 filter
-regularity thresholds for a generalized Gross-Pitaevskii equation: dispersive blow-up vs. nonlinear stability
Joannis Alexopoulos
We study a generalized Gross-Pitaevskii equation arising in the mean-field description of exciton-polariton Bose-Einstein condensates. The dynamics close to macroscopic wave functi…
Nonlinear dynamics of reaction-diffusion wave trains under large and fully nonlocalized modulations
Joannis Alexopoulos, Björn de Rijk
We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initia…
Nonlinear dynamics of periodic Lugiato-Lefever waves against sums of co-periodic and localized perturbations
Joannis Alexopoulos
In recent years, essential progress has been made in the nonlinear stability analysis of periodic Lugiato-Lefever waves against co-periodic and localized perturbations. Inspired by…
Nonlinear stability of periodic wave trains in the FitzHugh-Nagumo system against fully nonlocalized perturbations
Joannis Alexopoulos, Björn de Rijk
Recently, a nonlinear stability theory has been developed for wave trains in reaction-diffusion systems relying on pure -estimates. In the absence of localization of pert…