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.
arXiv commentIn 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 (15)
- Nonlocalized modulation of periodic reaction diffusion waves: Nonlinear stability
- Slow modulations of periodic waves in Hamiltonian PDEs, with application to capillary fluids
- Full description of Benjamin-Feir instability of Stokes waves in deep water
- Absence of shocks for 1D EULER-POISSON system
- High-Frequency Instabilities of Stokes Waves
- Spectral Stability of Inviscid Roll Waves
- Unstable Stokes waves
- Nonlinear Modulational Instability of Dispersive PDE Models
- Long-term regularity of the periodic Euler--Poisson system for electrons in 2D
- Modulated equations of Hamiltonian PDEs and dispersive shocks
- Co-periodic stability of periodic waves in some Hamiltonian PDEs
- Stability and instability in scalar balance laws: fronts and periodic waves
- Orbital stability via the energy-momentum method: the case of higher dimensional symmetry groups
- Linear Stability of solitary waves for the isothermal Euler-Poisson system
- Spectral instability of small-amplitude periodic waves of the electronic Euler-Poisson system