# Dispersive shocks and spectral analysis for linearized Quantum Hydrodynamics

## TL;DR

This paper analyzes the spectral properties and stability of dispersive shocks in a 1-D quantum hydrodynamics model, focusing on quantum effects via the Bohm potential and using spectral analysis techniques.

## Contribution

It provides a spectral analysis of linearized quantum hydrodynamics with dispersive effects, including stability assessment using the Evans function method.

## Key findings

- Spectral stability of dispersive shocks established.
- Linearized operator computed explicitly.
- Quantum effects influence shock stability characteristics.

## Abstract

In this paper we perform the analysis of spectral properties of the linearized system around constant states and dispersive shock for a 1-D compressible Euler system with dissipation--dispersion terms. The dispersive term is originated by the quantum effects described through the Bohm potential, as customary in Quantum Hydrodynamic models. The analysis performed in this paper includes the computation of the linearized operator and the spectral stability through the Evans function method.