  It is well known that the KdV equation has an infinite set of conserved
quantities. The first three are often considered to represent mass, momentum
and energy. Here we try to answer the question of how this comes about, and
also how these KdV quantities relate to those of the Euler shallow water
equations. Here Luke's Lagrangian is helpful. We also consider higher order
extensions of KdV. Though in general not integrable, in some sense they are
almost so.
