Supernonlinear ion-acoustic waves in a dusty plasma

An exact solution is obtained for the equations that describe nonlinear ion-acoustic waves in a dusty plasma. It is shown that the solution can be in the form of nonlinear periodic waves, solitons, and supernonlinear waves whose trajectories envelope one or several separatrices in the phase portrait of the wave. Profiles of physical quantities in the wave are constructed. The supernonlinear waves are shown to be of two types, subsonic (type 1) and supersonic (type 2). Existence regions of supernonlinear waves of both types and solitons are constructed in the plane of the problem parameters.