Lagrangean formulation of ion- and dust-ion-acoustic waves

Ion-acoustic modes propagating in unmagnetized dusty plasmas are studied by applying a generic collisionless fluid model. An Eulerian-to-Lagrangean variable transformation leads to a new system of evolution equations, which may be combined into a single (rather complex) equation for the mean ion density. The linear and weakly nonlinear oscillations regimes are studied and their modulational stability is investigated. This study extends known previous results on the Lagrangian description of electron- or ion-acoustic electrostatic plasma modes. The relevance with the description of dust-ion acoustic waves propagating in a dusty plasma is also discussed.