Nonlinear propagation of dust-acoustic modes in a dusty plasma with the Kappa-Cairns polarization force effects

Abstract

In this paper, the influence of Kappa-Cairns polarization force on solitary and periodic dust-acoustic (DA) waves is studied in a non-uniform dusty plasma containing negatively charged dust grains, Maxwellian electrons, and the Kappa-Cairns distributed ions. It is observed that in the presence of Kappa-Cairns distributed ions, the magnitude of the polarization force first increases as the spectral index increases and then decreases. The nonlinear Korteweg-de-Vries (K-dV) equation is obtained employing the reductive perturbation technique. The effects of polarization parameter (), Kappa-Cairns distribution parameters ( and ), and different ratios of ion to electron number densities () are investigated on the characteristics of DA solitary waves. We observed that the variations in the phase speed, amplitude, and width of DA solitons in the presence of the Kappa-Cairns polarization force are considerably different for case with respect to . The bifurcation theory of planar dynamical systems is also applied to investigate the existence of the solitary/periodic traveling wave in this plasma model. The phase portrait topology is illustrated for the K-dV equation. It is found that polarization force and other plasma parameters have a vital role in the traveling wave structures.