Introductory remarks

Abstract

This Discussion Meeting is devoted to the task of summarizing, consolidating and bringing into a self-consistent state the knowledge which exists in a relatively new area of study of the mechanics of waves, an area in which most of the work has been done during the past six years. This work, on dispersive systems, represents the second phase of development of the nonlinear mechanics of waves. The first phase, which is now more than a century old, was concerned with isotropic, nondispersive waves, that is, waves (like sound waves, for example) where the velocity of propagation of small disturbances is independent both of wavelength and of the direction of propagation, although larger disturbances are influenced by nonlinear effects. That theory is in two parts, a general study of the continuous change in waveform that results from nonlinear effects, and special study of the discontinuities which appear (in the form of shock waves) and of how they fit into the continuous solutions.