Self-action of Spatially Bounded Waves Containing Shock Fronts

Abstract

The term self-action is used in wave physics primarily to characterize nonlinear phenomena, where an intense wave, without changing its shape, acquires amplitude-dependent absorption coefficient or propagation velocity. In the first case, one speaks of nonlinear absorption (or amplification) of the wave, whereas in the second case, one speaks of nonlinear dispersion. Note that precisely this permanence or slow variation of its shape allows one to consider the wave as a single whole entity with its own propagation velocity. Discovery of self-focusing of light brought about the first appreciable interest towards self-action effects. Historical background is described in detail in Refs [1,2]. In nonlinear optics, quasi-harmonic waves are stable objects. Their stability appears due to strong dispersion, which prevents generation of waves at other frequencies, i.e. distortion of the profile of the original wave. Self-action of waves is connected with the response of a medium at the fundamental frequency; this response appears due to cubic and higher-order odd nonlinearities of the medium. Note, however, that while considering coupled waves at different frequencies, self-action may also occur in a quadratically nonlinear medium.