We investigate the possibility for dust ion-acoustic solitons to exist. Compressive solitonlike perturbations are damped and slowed down, mainly due to the plasma absorption and ion scattering on microparticles. The perturbations are shown to possess the main properties of solitons. There is a principal possibility to study experimentally the role of trapped electrons in the soliton formation.

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Nonlinear electrostatic wave structures in dusty plasmas in the presence of electromagnetic radiation are investigated. The dust charge variation is assumed to be caused by microscopic electron and ion currents at the grains as well as photoelectric current of electrons. Calculations of electromagnetic radiation effects are performed for the case of solar radiation spectrum in the vicinity of the earth. The exact solutions of the nonlinear equations, describing variable-charge dust grains, Boltzmann electrons, and inertial ions, are obtained in the form of steady-state shocks. The conditions for their existence are found. The dissipation in such shock waves originates from the process of dust charging. The possibility of observation of shock waves related to the dust charging process in the presence of electromagnetic radiation in active rocket experiments which involve the release of some gaseous substance in near-earth space is discussed

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