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Research Article | Open Access

Numerical spectral analysis of standing waves in quantum hydrodynamics with viscosity

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

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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.

Keywords

quantum hydrodynamicsstanding wavesspectral instability

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Mathematics in Engineering
Volume 6 Issue 3,
June 2024
Pages 407-424
DOI: 10.3934/mine.2024017

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Cite this article:
Zhelyazov D. Numerical spectral analysis of standing waves in quantum hydrodynamics with viscosity. Mathematics in Engineering, 2024, 6(3): 407-424. https://doi.org/10.3934/mine.2024017

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Received: 31 January 2024
Revised: 14 May 2024
Accepted: 17 May 2024
Published: 28 May 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)