Numerical spectral analysis of standing waves in quantum hydrodynamics with viscosity

Delyan Zhelyazov; Delyan Zhelyazov

doi:10.3934/mine.2024017

Mathematics in Engineering

2024, Volume 6, Issue 3: 407-424. doi: 10.3934/mine.2024017

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Numerical spectral analysis of standing waves in quantum hydrodynamics with viscosity

Delyan Zhelyazov ^{§
,
,}

Departamento de Matemáticas y Mecánica, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Circuito Escolar s/n, Ciudad Universitaria, C.P. 04510, Cd. Mx., Mexico
^§Current address: Department of Mathematics, University of Surrey, Guildford, United Kingdom

Received: 31 January 2024 Revised: 14 May 2024 Accepted: 17 May 2024 Published: 28 May 2024

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.
- quantum hydrodynamics,
- standing waves,
- spectral instability
Citation: Delyan Zhelyazov. Numerical spectral analysis of standing waves in quantum hydrodynamics with viscosity[J]. Mathematics in Engineering, 2024, 6(3): 407-424. doi: 10.3934/mine.2024017

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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.

References

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