Numerical spectral analysis of standing waves in quantum hydrodynamics with viscosity

2024/05/22 by Delyan Zhelyazov, Zhelyazov, Delyan
Earth and Planetary Sciences · Engineering · #Analysis of PDEs (math.AP) #Chaotic Dynamics (nlin.CD) #Coastal and Marine Dynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics Simulations and Interactions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2405.13917

openalex publication_date 2024/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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