Nonlinear Waves of Envelopes: Glimpses of History

Presented by Lev Ostrovsky - University of Colorado and University of North Carolina, USA, and Institute of Applied Physics, Russian Acad. Sci.

Abstract: The 1960-70s witnessed a fast development of the science of nonlinear waves. They can often be called modulated waves meaning that the parameters of “fast” oscillations in time and space, 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.” The applications have mostly related to two areas: the surface water waves and, after creation of a laser in 1960, the nonlinear optics. This presentation outlines some aspects of these early studies, having occurred in parallel in different groups, especially in Britain and Soviet Union.  It refers to such effects as self-phase modulation, self-steepening of an envelope, averaged variational principle, modulational instability, and envelope solitons.