In this paper, the quantum hydrodynamics (QHD) model is used to study the propagation of small- but finite-amplitude quantum electrostatic shock-wave in an inertial-less symmetric pair (ion) plasma with immobile background positive constituents. The dispersion due to the quantum tunneling and inertial effects as well as dissipation caused by particle collisions leading to the shock-like or double-layer structures are considered. Investigation of both the stationary and traveling-wave solutions to Kortewege-de Veries-Burgers evolution equation show that critical values exist which govern the type of collective plasma structures. Current analysis apply to diverse kind of symmetric plasmas such as laboratory inertially confined or astrophysical pair-ion or electron-positron degenerate plasmas.
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