Nonstationary nonlinear dust-acoustic waves in unmagnetized plasma

Abstract

The nonstationary and nonlinear dust-acoustic wave is considered in the framework of the Lagrangian fluid description. A single nonlinear equation and its solutions are obtained for dust-acoustic waves with nontrivial space and time dependence in both the large and small amplitude limit. In the absence of linear dispersion solutions in the large amplitude limit, it is demonstrated that under well-defined initial and boundary conditions the amplitude of the solutions is decreasing and the spatial profile spreads. This is a new class of nonlinear solutions leading to short-lived nonlinear structures. In the small amplitude limit, the soliton-like solution indicates close association with Korteweg–de Vries solitons.