ON THE DERIVATION OF FLUXES FOR CONSERVATION-LAWS IN HAMILTONIAN-SYSTEMS

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.