Large scale instability of nonlinear standing waves

Abstract

We present the nonlinear phase equations describing the stability of a time-periodic one-dimensional spatial pattern, that arises in a system which is invariant by space and time translations and space reflection symmetry. We show that a large scale oscillatory instability can occur, leading to a quasiperiodic temporal regime with two different spatial scales On etablit les equations aux derivees partielles non lineaires qui gouvernent la stabilite a grande echelle d'une structure cellulaire unidimensionnelle oscillante, apparaissant dans un systeme hors equilibre, invariant par translations d'espace et de temps, et par reflexion d'espace. Existence d'une instabilite oscillatoire, conduisant a un regime quasi periodique, possedant deux echelles spatiales distinctes