Abstract

The 1960s-70s witnessed a fast development of the science of nonlinear waves. In particular, it refers to modulated waves in which the parameters of oscillations such as amplitude, frequency, and wavenumber, are slowly varying, and these variations can themselves propagate as nonlinear waves that can (albeit loosely) be called “waves of envelopes” or “waves of modulation.” The applications were mostly related to two areas: the surface water waves, and nonlinear electromagnetic waves in transmission (delay) lines, and, of course, in optical systems under the action of lasers. The works in the first area began in UK and USA , and they are well known to this audience. Here we will concentrate on the theory of modulated electromagnetic waves, which began to be developed in the former Soviet Union, parallel to the Western works on water waves. This presentation outlines some aspects of these studies, including such effects as self-phase modulation, self-steepening of an envelope, modulation instability, and envelope solitons, bright and dark. Whenever possible, the corresponding experimental results are shown.