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The paper concerns with the stability of periodic travelling waves of dnoidaltype of the Zakharov system. This problem was considered in Angulo-Brango,Nonlinearity'11, where it was shown that subject to a technical condition onthe perturbation, such waves are orbitally stable, with respect toperturbations of the same period. Our main result fills up the gap created bythe aforementioned technical condition. More precisely, we show that for allnatural values of the parameters, the periodic dnoidal waves are spectrallystable.

Spectral stability of periodic waves for the Zakharov system