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The propagation of weakly nonlinear dust--acoustic waves in a dusty plasmacontaining two ion species with different temperatures is explored. Thenonlinear equations describing both the quadratic and cubic plasmanonlinearities are derived. It is shown that the properties of dust--acousticwaves depend substantially on the grain size distribution. In particular, forsolitary dust--acoustic waves with a positive potential to exist in a plasmawith distributed grain size, it is necessary that the difference between thetemperatures of two ion species be large that that in the case of unusizedgrains.

Solitary Dust--Acoustic Waves in a Plasma with Two-Temperature Ions and Distributed Grain Size