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

Abstract

Arbitrary amplitude dust acoustic waves(DAWs) in a quantum dusty plasma including the effect of dust size distribution (DSD) is presented. By using the Sagdeev pseudopotential method for large amplitude waves, the energy integral is derived which includes Sagdeev potential. By applying the conditions in which a solitary solution can be existed, the upper and lower limits of Mach number is presented. 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 having power law size distribution, the solitary waves transform into cnoidal ones.. The phase portrait is also plotted and comprised of Two different sets of orbits, a periodic orbit and a homoclinic one that correspond to periodic traveling wave solution and solitary wave solution, respectively

Keywords

• quantum dusty plasma
• dust acoustic waves
• dust size distribution
• sagdeev pseudo potential method