title: Instability criteria and pattern formation in the complex Ginzburg-Landau equation with higher-order terms.
abstract: We study the modulational instability and spatial pattern formation in extended media, taking the one-dimensional complex Ginzburg-Landau equation with higher-order terms as a perturbation of the nonlinear Schrödinger equation as a model. By stability analysis for the original partial differential equation, we derive its stability condition as well as the threshold for amplitude perturbations and we show how nonlinear higher-order terms qualitatively change the behavior of the system. The analytical results are found to be in agreement with numerical findings. Modulational instability mediates pattern formation through the lattice. The main feature of the traveling plane waves is its disintegration in pulse train during the propagation through the system.
authors.affiliation: Laboratory of Mechanic, Department of Physics, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon.
authors.forename: Alidou
authors.initials: A
authors.lastname: Mohamadou
authors.forename: Bebe Emilienne
authors.initials: BE
authors.lastname: Ayissi
authors.forename: Timoléon Crépin
authors.initials: TC
authors.lastname: Kofané