Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity

Corrado Lattanzio; Delyan Zhelyazov

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arXiv · 2103.10386

Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity

Corrado Lattanzio·Delyan Zhelyazov

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Abstract

In this paper we investigate spectral stability of traveling wave solutions to 1-$D$ quantum hydrodynamics system with nonlinear viscosity in the $(\rho,u)$, that is, density and velocity, variables. We derive a sufficient condition for the stability of the essential spectrum and we estimate the maximum modulus of eigenvalues with non-negative real part. In addition, we present numerical computations of the Evans function in sufficiently large domain of the unstable half-plane and show numerically that its winding number is (approximately) zero, thus giving a numerical evidence of point spectrum stability.

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Corrado Lattanzio, Delyan Zhelyazov. 2021-03-18. Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity. https://arxiv.org/abs/2103.10386

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