Spectral instability of small-amplitude periodic waves of the electronic Euler-Poisson system
arXiv:2210.10118 · doi:10.1088/1361-6544/ace604
Abstract
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 and, beyond specific computations, newly devised arguments. The growth rate with respect to the amplitude of the background waves is also provided when the instability occurs.
In this new version, we carried out some simulations on the shapes of spectral curves around second to fourth crossing and find that they form instability bubbles asymptotically shaped as an ellipse. This version represents a comprehensive and detailed version of the forthcoming paper to appear in the journal "Nonlinearity."
References in corpus (5)
- Full description of Benjamin-Feir instability of Stokes waves in deep water
- High-Frequency Instabilities of Stokes Waves
- Unstable Stokes waves
- Linear Stability of solitary waves for the isothermal Euler-Poisson system
- Spectral instability of small-amplitude periodic waves of the electronic Euler-Poisson system