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Possibility for dust ion-acoustic solitons to exist in complex (dusty) plasmas in the presence of electromagnetic radiation, which results in positive dust particle charges, is investigated. Dissipative processes occurring during the propagation of dust ion-acoustic perturbations, among which are the charging of dust grains, the absorption of ions by grains, the transfer of the ion momentum to the grains, and ion-neutral collisions, are taken into account. Temporal evolution of the soliton-like perturbation and interaction of two soliton-like perturbations are studied. Compressive soliton-like perturbations are shown to possess the main properties of the soltons, in particular, the interacting perturbations conserve their form.

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