With two-temperature ions in dusty plasma, the effects of variable dust charge on small-amplitude dust-acoustic solitons and large-amplitude dust-acoustic solitary waves are investigated. It is found that both compressive and rarefactive solitons (and solitary waves), as well as double layers, exist. The introduced small, but finite, number density of the lower temperature ions provides the possibility of the coexistence of large-amplitude rarefactive with compressive dust-density solitary waves. The amplitudes of those dust-density solitary waves become smaller and the regime of Mach number is extended wider for the variable dust charge situation compared to the constant dust charge situation.

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