The effect of linear ion Landau damping on weakly nonlinear as well as weakly dispersive low-frequency waves in a dusty plasma is investigated. The standard perturbative approach leads to the Korteweg-de Vries (KdV) equation with a linear Landau damping term for the dynamics of the low-frequency nonlinear wave. Landau damping causes the wave amplitude to decay with time and the dust charge variation enhances the damping rate.

The effects of ion-neutral collision on the electrostatic wave packets in the absence of the magnetic field in a pair-ion plasma have been investigated. Considering a two-fluid plasma model with the help of the standard perturbation technique, two distinct electrostatic modes have been observed, namely, a low-frequency ion acoustic mode and a high-frequency ion plasma mode. The dynamics of the modulated wave is governed by a damped nonlinear Schrödinger equation. Damping of the soliton occurs due to the ion-neutral collision. The analytical and numerical investigation reveals that the ion acoustic mode is both stable and unstable, which propagates in the form of dark solitons and bright solitons, respectively, whereas the ion plasma mode is unstable, propagating in the form of a bright soliton. Results are discussed in the context of the fullerene pair-ion plasma experiments.

Nonlinear propagation of magnetosonic shock wave has been studied in collisional magnetized pair-ion plasma. The masses of both ions are same but the temperatures are slightly different. Two fluid model has been taken to describe the model. Two different modes of the magnetosonic wave have been obtained. The dynamics of the nonlinear magnetosonic wave is governed by the Korteweg-de Vries Burgers' equation. It has been shown that the ion-ion collision is the source of dissipation that causes the Burgers' term which is responsible for the shock structures in equal mass pair-ion plasma. The numerical investigations reveal that the magnetosonic wave exhibits both oscillatory and monotonic shock structures depending on the strength of the dissipation. The nonlinear wave exhibited the oscillatory shock wave for strong magnetic field (weak dissipation) and monotonic shock wave for weak magnetic field (strong dissipation). The results have been discussed in the context of the fullerene pair-ion plasma experiments.