In this paper, we investigate spectral stability of traveling wave solutions to 1D quantum hydrodynamics system with nonlinear viscosity in the (ρ,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.

中文翻译：

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非线性黏度量子流体动力学色散冲击的谱分析

在本文中，我们研究了具有非线性粘度的一维量子流体动力学系统的行波解的光谱稳定性。(ρ,你)，即密度和速度，变量。我们推导出了基本谱稳定性的充分条件，并估计了具有非负实部的特征值的最大模量。此外，我们提出了在不稳定半平面的足够大域中的 Evans 函数的数值计算，并在数值上表明它的绕组数（大约）为零，从而给出了点谱稳定性的数值证据。