Periodic nonlinear dust-acoustic waves in multispecies dusty plasmas

A pseudopotential analysis is presented for the propagation of nonlinear periodic dust-acoustic waves in a dusty plasma comprising cold negative dust, Boltzmann electrons, and Boltzmann or Cairns nonthermal positive ions, extending thus earlier treatments for ion-acoustic waves in electron–proton plasmas. The dusty plasma model where both electrons and ions are Boltzmann does not admit solitons, but works for nonlinear periodic waves. For consistency in the periodic case, two properties are required: conservation per cycle of species densities and that for very small amplitudes the waves resemble linear waves. The first property has to be imposed through a global perturbation of the undisturbed equilibrium, whereas the second property follows naturally from the formalism. After obtaining the general analytical methodology, a numerical analysis is discussed and illustrated with graphs for the electrostatic potential profile, the Sagdeev pseudopotential, the wave electric field, and the three different species densities, first for the Boltzmann and thereafter for the Cairns ions.