Shallow-water waves, the Korteweg-deVries equation and solitons

Abstract

A comparison of laboratory experiments in a shallow-water tank driven by an oscillating piston and numerical solutions of the Korteweg-de Vries (KdV) equation show that the latter can accurately describe slightly dissipative wavepropagation for Ursell numbers ( h 1 L 2 / h 0 3 ) up to 800. This is an input-output experiment, where the initial condition for the KdV equation is obtained from upstream (station 1) data. At a downstream location, the number of crests and troughs and their phases (or relative locations within a period) agree quantitatively with numerical solutions. The crest-to-trough amplitudes disagree somewhat, as they are more sensitive to dissipative forces. This work firmly establishes the soliton concept as necessary for treating the propagation of shallow-water waves of moderate amplitude in a low-dissipation environment.