Self-action effects for wave beams containing shock fronts

Abstract

The review covers experimental and theoretical studies of the self-action effects observed for intense wave beams with sawtooth time profiles. For sawtooth waves inquadratic nonlinear media, inertial self-focusing and defocusing processes caused by the formation of acoustic streaming and heating due to nonlinear energy dissipation at shock fronts are discussed. Self-refraction of shock-wave pulses is considered,which leads, in particular, to the saturation of the maximal field achieved by focusing. For cubic nonlinear media, where a sawtooth wave contains both compression and rarefaction shocks, the self-focusing process is studied in the presence of its strongcompetition with nonlinear damping. New mathematical models, their symmetry properties and exact solutions, and the results of numerical simulation are described. A general picture of the state of the art in this field is given.