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We prove existence of standing waves for two quantum hydrodynamics systemswith linear and nonlinear viscosity. Moreover, global existence of travelingwaves is proved for the former without restrictions on the viscosity anddispersion parameters, thanks to a suitable Lyapunov function. This is animprovement with respect to the global existence result in \cite{LMZ2020},where it was required that the viscosity is sufficiently strong.

Existence of standing and traveling waves in quantum hydrodynamics with viscosity