Matter Transport as Fundamental Property of KdV Solitons in Shallow Water

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