Linear and nonlinear dust ion acoustic waves in ultracold quantum dusty plasmas

By considering the one-dimensional quantum hydrodynamic model for a three-species ultracold quantum dusty plasma, the properties of dust-ion-acoustic waves are studied. The dispersion relation in the linear regime and the Korteweg-de Vries equation in the nonlinear regime are derived by incorporating quantum corrections. The quantum-mechanical effects through quantum diffraction and quantum statistics as well as the role of immobile charged dust particulates are studied both analytically and numerically. It is found that the amplitude and width of the dust ion acoustic solitary waves are significantly affected by the quantum corrections and concentration of the dust particles.