Dust ion-acoustic rogue waves in a three-species ultracold quantum dusty plasmas

• The nonlinear Schrödinger equation is derived for the low frequency limit.
• Modulational instability growth rate is discussed.
• The first- and second-order dust ion-acoustic rogue waves are examined numerically.

Dust ion-acoustic (DIA) rogue waves are reported for a three-component ultracold quantum dusty plasma comprised of inertialess electrons, inertial ions, and negatively charged immobile dust particles. The nonlinear Schrödinger (NLS) equation appears for the low frequency limit. Modulation instability (MI) of the DIA waves is analyzed. Influence of the modulation wave number, ion-to-electron Fermi temperature ratio ρρ and dust-to-ion background density ratio NdNd on the MI growth rate is discussed. The first- and second-order DIA rogue-wave solutions of the NLS equation are examined numerically. It is found that the enhancement of NdNd and carrier wave number can increase the envelope rogue-wave amplitudes. However, the increase of ρρ reduces the envelope rogue-wave amplitudes.