Some Special Cases Treated by the Whitham Theory

Abstract

The theory of the preceding paper (by G. B. Whitham) may be valuable in problems of nonlinear dispersive wave systems governed by equations too complicated for analytical or numerical treatment. It suggests, in fact, that the development of wave groups, whose parameters vary gradually enough, can be represented by much less complicated approximate equations, derived from the assumption that in each separate small region the waves are closely like plane periodic ones. Nevertheless, the effort demanded to solve even those approximate equations would normally be very substantial, and therefore it is important (see §1) to get a preliminary idea of whether the solutions would correspond well with reality or not, by calculating the implications of the theory in detail for some rather simple system or systems and comparing them with experiment.