  In a semiconductor superlattice with long scattering times, damping of Bloch
oscillations due to scattering is so small that nonlinearities may compensate
it and Bloch oscillations persist even in the hydrodynamic regime. To
demonstrate this, a Boltzmann-Poisson transport model of miniband superlattices
with inelastic collisions is proposed and hydrodynamic equations for electron
density, electric field and the complex amplitude of the Bloch oscillations are
derived by singular perturbation methods. For appropriate parameter ranges,
numerical solutions of these equations show stable Bloch oscillations with
spatially inhomogeneous field, charge, current density and energy density
profiles. These Bloch oscillations disappear as scattering times become
sufficiently short. For sufficiently low lattice temperatures, Bloch and Gunn
type oscillations mediated by electric field, current and energy domains
coexist for a range of voltages. For larger lattice temperatures (300 K), there
are only Bloch oscillations with stationary amplitude and electric field
profiles.
