effect of diffraction parameter on ultra relativistic dust-ion-acoustic waves in a quantum dusty plasma

The existence of both fast (compressive) and slow (rarefactive) solitons on the dust-ion-acoustic waves (diaws) is investigated considering quantum hydrodynamic (qhd) model with a three-components quantum dusty plasma and relativistic effects  using the korteweg–de vries (kdv) equation. the impact of different plasma parameters like quantum diffraction parameter , ion to electron fermi temperature ratio , dust concentration , and the relativistic factor  is also discussed. the relativistic effect  demonstrates higher amplitude of the solitons than the relativistic effect . from the results, dispersive property of quantum dusty plasma is strongly related to the quantum parameter . additionally, it is noticed that the ranges of quantum parameter  for the fast and slow modes, respectively, are significantly impacted by the dust concentration. applications for the plasma model, which has inertialess electrons, very negatively charged dust grains, and ultrarelativistic positive ions, include fusion research and astrophysics.