  We couple a nonlinear evolution equation with an associated one and derive
the action principle. This allows us to write the Lagrangian density of the
system in terms of the original field variables rather than Casimir potentials.
We find that the corresponding Hamiltonian density provides a natural basis to
recast the pair of equations in the canonical form. Amongst the case studies
presented the KdV and modified KdV pairs exhibit bi-Hamiltonian structure and
allow one to realize the associated fields in physical terms
