The use of Noether's theorem and Lie-group techniques provides a syste
matic method for investigating the conservation laws of evolution equa
tions, that is, expressions of the form DtT + div F = 0. For Hamiltoni
an systems, the method gives only the density T, and the flux F must b
e computed indirectly using the evolution equations. Here, a direct pr
ocedure for calculating the flux is developed based on the density of
the conserved quantity and on the associated symmetry generator. Simpl
e expressions are given for specific classes of conservation laws. Par
ticular attention is paid to Hamiltonian systems involving non-local o
perators.