Context. Most theoretical investigations of wave phenomena in dusty plasmas have treated charged dust as additional heavy negativeions in standard multispecies models. Many dusty plasma experiments use monodisperse grains, but charged (and neutral) grains inspace environments come in a whole range of sizes and compositions, hence in masses and charges. Dust density distributions havinga power-law decay with size are often observed in planetary rings.Aims. There is a need to investigate larger solitary structures, since wave descriptions involving charged dust distributions have usu-ally been limited to linear or weakly nonlinear modes.Methods. Sagdeev pseudopotential methods describe large-amplitude solitary waves in a co-moving reference frame and are adaptedto include dust distributions, using mass and charge, or alternatively size, as additional variables. Observed power-law distributionslead to descriptions involving hypergeometric functions.Results. Lower limits for possible solitary wave velocities follow from requiring that the Sagdeev pseudopotentials have a local max-imum for the undisturbed conditions, whereas upper limits come from ensuring that dust densities remain real. Nonlinear amplitudesincrease with solitary wave velocities and relative electron temperature. Under similar plasma conditions, dust size distributions ad-mit slower solitary wave solutions, with correspondingly smaller amplitudes than given by monodisperse dust models. For typicalplanetary ring conditions, the difference can be quite appreciable.
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