Ion holes in dusty pair plasmas

The existence of Bernstein-Greene-Kruskal (BGK)-like trapped ion modes in dusty plasmas is investigated by means of the pseudo-potential method applied to the Vlasov-Poisson system. The nonlinear dispersion relation, determining the phase velocity, and the pseudo-potential, representing the wave form and hence its spectral decomposition, are derived and analysed with respect to the effect of dust. Dust is found to diminish the region in ω, k-space, where periodic wave solutions of fast and slow mode character exist. Localized wave solutions in the form of solitary ion holes, owing their existence to the presence of dust, coexist as well, but turn into slow ion acoustic double layers in the limit of vanishing dust.