Spectral stability of periodic waves for the Zakharov system

Abstract

This paper is concerned with the stability of periodic traveling waves of dnoidal type, of the Zakharov system. This problem was considered in a study of Angulo and Brango [Nonlinearity 24, 2913 (2011)]. In particular, it was shown that under a technical condition on the perturbation, such waves are orbitally stable, with respect to perturbations of the same period. Our main result fills up the gap created by the aforementioned technical condition. More precisely, we show that for all natural values of the parameters, the periodic dnoidal waves are spectrally stable.