Matter Transport as Fundamental Property of KdV Solitons in Shallow Water

Abstract

Using the Korteweg-De Vries equation (KdV), the velocities of the fluid motion inside the soliton are calculated. It is shown that the horizontal component of the fluid velocity is always greater than zero, corresponding to the unidirectional transport of matter by the soliton. The fluid mass is transported by the soliton for a finite distance in the direction of its motion, and this mass is calculated as a function of its amplitude. It is also shown that the matter transport cannot be neglected for solitons of arbitrary amplitude.