A four-component dusty plasma consisting of electrons, ions, and negative as well as positive dust particles has been considered. The basic properties of small but finite amplitude solitary potential structures that may exist in such a four-component dusty plasma have been investigated theoretically by the reductive perturbation method. It has been found that the presence of additional positive dust component has significantly modified the basic properties of solitary potential structures in a dusty plasma. The implications of our results in different regions of space (viz., cometary tails, mesosphere, Jupiter’s magnetosphere, etc.) are discussed briefly.

Properties of small but finite amplitude dust ion-acoustic (DIA) solitary waves in a dusty plasma composed of inertialess electrons, positive and negative inertial ions, and immobile negative/positive charged dust grains are investigated. By using the multifluid dusty plasma model, the Kortweg-de Vries equation and energy integral for small and large amplitude solitary pulses, are derived. It is found that the presence of the negative ions modifies the properties of the solitary DIA waves, and provides the possibility of positive and negative solitary potential structures to coexist. The present results may be useful for understanding the salient features of localized DIA excitations that may appear in data from forthcoming laboratory experiments and space observations

The properties of dust ion-acoustic shock waves in an unmagnetized dusty plasma, whose constituents are adiabatic ion fluid, Boltzmann electrons, and static dust, are investigated by employing the reductive perturbation method. The Burgers equation is derived and its stationary analytical solution is numerically analyzed. It has been found that both the amplitude and the width decrease with the increase of the ion-fluid temperature. The implications of our results in space and laboratory dusty plasmas are briefly discussed.

A rigorous theoretical investigation has been made of dust-acoustic (DA) Korteweg–de Vries (K-dV) solitons by the reductive perturbation method. An unmagnetized dusty plasma consisting of negatively charged adiabatic hot dust fluid and of Boltzmann distributed electrons and ions has been considered. It has been found that the DA K-dV solitons associated with only negative potential can exist in such a dusty plasma. It has been also found that the effects of dust fluid temperature have significantly modified the basic properties (amplitude and width) of the solitary potential structures in such a dusty plasma. The implications of these results to some space and astrophysical plasma situations are briefly discussed.

A formalism for treating modulational interactions of electrostatic fields in collisionless quantum plasmas is developed, based on the kinetic Wigner-Poisson model of quantum plasma. This formalism can be used in a range of problems of nonlinear interaction between electrostatic fields in a quantum plasma, such as development of turbulence, self-organization, as well as transition from the weak turbulent state to strong turbulence. In particular, using this formalism, we obtain the kinetic quantum Zakharov equations, that describe nonlinear coupling of high frequency Langmuir waves to low frequency plasma density variations, for cases of non-degenerate and degenerate plasma electrons.