Spectral instability of small-amplitude periodic waves of the electronic Euler-Poisson system
Résumé
The present work shows that essentially all small-amplitude periodic traveling waves of the electronic Euler-Poisson system are spectrally unstable. This instability is neither modulational nor co-periodic, and thus requires an unusual spectral analysis. The growth rate with respect to the amplitude of the background waves is also provided when the instability occurs. We expect that the corresponding newly devised arguments could have a broad scope of application.