  It is shown that a set of functions which characterise the Lax hierarchy of
non-linear equations may be represented in terms of the eigenstates of the
potential which satisfies the generalised KdV equation. Such a representation
leads to sumrules relating integrals involving the soliton potential and its
various derivatives to sums involving the boundstate eigenvalues of the
Schroedinger equation for the reflectionless potential. A new hierarchy of
functions, which is in a sense dual to the Lax hierarchy, is identified. It is
shown that time dependent equations involving the dual functions may be
established which permit solutions related to an N-soliton structure similar to
that for the Lax hierarchy but with a different 'speed' for the solitons.
