@article{Zhelyazov2024, 
author = {Delyan Zhelyazov},
title = {Numerical spectral analysis of standing waves in quantum hydrodynamics with viscosity},
year = {2024},
journal = {Mathematics in Engineering},
volume = {6},
number = {3},
pages = {407-424},
keywords = {quantum hydrodynamics, standing waves, spectral instability},
url = {https://www.sciopen.com/article/10.3934/mine.2024017},
doi = {10.3934/mine.2024017},
abstract = {We study the spectrum of the linearization around standing wave profiles for two quantum hydrodynamics systems with linear and nonlinear viscosity. The essential spectrum for such profiles is stable; we investigate the point spectrum using an Evans function technique. For both systems we show numerically that there exists a real unstable eigenvalue, thus providing numerical evidence for spectral instability.}
}