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.
Numerical spectral analysis of standing waves in quantum hydrodynamics with viscosity / Zhelyazov, Delyan. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - 6:3(2024), pp. 407-424. [10.3934/mine.2024017]
Numerical spectral analysis of standing waves in quantum hydrodynamics with viscosity
Zhelyazov, Delyan
2024-01-01
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.File in questo prodotto:
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