Self-action effects for wave beams containing shock fronts

The review covers experimental and theoretical studies of the self-action effects observed for intense wave beams with sawtooth time profiles. For sawtooth waves in quadratic 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 strong competition 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.