5 papers
-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…
Uniformity in the Fourier inversion formula with applications to Laplace transforms
Joannis Alexopoulos
We systematically find conditions which yield locally uniform convergence in the Fourier inversion formula in one and higher dimensions. We apply the gained knowledge to the comple…
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…