Effect of nonthermal and nonextensive electrons on dust acoustic waves in planetary rings

Dust acoustic waves (DAWs) in plasmas are influenced by many plasma parameters, such as, ion temperature, electron number density, nonthermal and nonextensive parameters, and dust cyclotron frequency. The plasma system is described by plasma fluid equations. The Zakharov–Kuznetsov equation and instability growth rate of DAWs have been obtained by reductive perturbation method and small-$k$ expansion method, respectively. The effects of plasma parameters on the linear dispersion relation, phase velocity, amplitude, width, soliton energy, and three-dimensional instability of DAWs have been carried out. It is obvious that the incremental nonextensive (nonthermal) parameter leads to the shrinking (incremental) soliton energy and phase velocity. These results are useful for understanding dusty plasma dynamics with Cairns–Tsallis electrons in planetary rings.