Nonlinear propagation of quantum dust-ion acoustic shock and solitary waves in an unmagnetized and collisionless four-component plasma medium containing inertialess quantum electrons and positrons, and also classical ions and stationary negative dust grains, which are affected by dust charge variations and viscosity of ions, are investigated using a quantum hydrodynamic model by employing the tanh method. The Korteweg–de Vries-Burgers and the Korteweg–de Vries equations indicate the behavior of shocks and solitons in this plasma model, respectively. Consideration of the dust charge variation requires the evaluation of charging currents. These currents are determined with the orbit limited motion theory and using the corresponding velocity distribution function. In the following, the effects of chemical potential and the density of dust grains on the structure of oscillatory and monotonic shock waves and solitary waves are investigated. The current study extends our understanding of the characteristics of quantum nonlinear structures in superdense astrophysical systems, inertial confinement fusion plasmas, and ultrasmall micro- and nano- electronic devices.

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