Nonlinear waves in multispecies self-gravitating dusty plasmas

We discuss the nonlinear evolution of electrostatic dust-acoustic waves in a uniform gravitating dusty plasma, when self-gravitation does not affect the linear behavior of the modes, but comes into play at the nonlinear level. This is valid for grains which are not too massive, as their charge-to-mass ratios are too high to make Coulomb and gravitational forces fully comparable. In our multispecies dusty plasma all species are treated alike, including pressure and gravitational effects. Afterwards we specialize our results to cold dust, in the presence of Boltzmann electrons and ions. The nonlinear behaviour is governed by an extended Korteweg-de Vries equation with a source term, similar in structure to the one describing perpendicular magnetosonic waves in a bi-ion plasma. It is a nonintegrable equation, so that no classic solitons or double layers are possible, although the equation could be tackled by perturbative iteration or by means of numerical analysis.