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The propagation of solitary waves in an unmagnetized collisional dusty plasma consisting of a negatively charged dust fluid, positively charged ions, isothermal electrons, and background neutral particles is studied. The ionization, ion loss, ion-neutral, ion-dust, and dust-neutral collisions are considered. Applying a reductive perturbation theory, a damped Korteweg-de Vries (DKdV) equation is derived. On the other hand, at a critical phase velocity, the dynamics of solitary waves is governed by a damped modified Korteweg-de Vries (DMKdV) equation. The nonlinear properties of solitary waves in the two cases are discussed.

Propagation characteristics of dust acoustic (DA) solitons in an opposite polarity dusty plasma medium containing inertial positive and negative dust grains and inertialess ions and electrons following Maxwellian distribution have been theoretically investigated by taking the effect of generalized polarization force into consideration. By using the reductive perturbation method, the Korteweg–de Vries equation that governs the nonlinear dust acoustic waves has been derived. It has been found that rarefactive and compressive solitons (solitons associated with negative and positive potentials) propagate in such a dusty plasma medium. The dependence of soliton characteristics on the system parameters has been discussed. It is observed that the basic properties of the DA solitons are significantly modified by the effects of generalized polarization force, ion-to-electron temperature ratio, and positive dust component. The findings of this investigation may be used in understanding the wave propagation in space and laboratory plasmas in which dust of opposite polarity coexists under the polarization force.

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The nonlinear propagation of dust ion-acoustic solitary waves (DIASWs) in a magnetized dusty plasma which consists of two different types of nonisothermal electrons, hot adiabatic inertial ions fluid and immobile negatively charged dust particles is studied. The modified Zakharov–Kuznetsov (MZK) equation, describing the small but finite amplitude DIASWs, is derived using a reductive perturbation method. The combined effects of the external magnetic field, obliqueness (i.e., the propagation angle), and the two-temperature nonisothermal electrons, which are found to significantly modify the basic properties of DIASWs, are explicitly examined. The three-dimensional instability of DIASWs is also analyzed using the small-k (long wavelength plane wave) perturbation expansion technique. The results show that the external magnetic field, the propagation angle, and the two-temperature nonisothermal electrons have strong effects on the instability criterion as well as the growth rate.