Arbitrary Amplitude Dust Acoustic Solitary Waves in a Quantum Dusty Plasma with Arbitrary Dust Size Distribution

Arbitrary amplitude dust acoustic waves (DAWs) in a quantum dusty plasma including the effect of the dust size distribution (DSD) are presented here. By using the Sagdeev pseudopotential method for large amplitude waves, the energy integral is derived which includes Sagdeev potential. The upper and lower limits of Mach number are presented, by applying the conditions in which a solitary solution can exist. Two cases are studied, a mono-sized dust grains case and dust grains possessing power-law size distribution case. The result shows that, the allowed Mach number’s range is increased for mono-sized dust grains case. Sagdeev potential is also plotted and it is seen that in mono-sized dust grains case, solitary waves are propagated. Whereas, for different-sized dust grains with power-law size distribution, the solitary waves transform into cnoidal ones.