Traveling waves for quantum hydrodynamics with nonlinear viscosity

In this paper we study existence of traveling waves for 1-D compressible Euler system with dispersion (which models quantum effects through the Bohm potential) and nonlinear viscosity in context hydrodynamic superfluidity. The profiles is proved appropriate (super– or sub– sonic) end states defining Lax shocks underlying formulated terms density velocity without restrictions parameters. On other hand, interplay plays a crucial role proving oscillatory profiles, showing way how significant certain regimes. Numerical experiments are also provided to analyze sensitivity such respect viscosity/dispersion nearness vacuum.