  There are many evolution partial differential equations which can be cast
into Hamiltonian form. Conservation laws of these equations are related to
one-parameter Hamiltonian symmetries admitted by the PDEs. The same result
holds for semidiscrete Hamiltonian equations. In this paper we consider
semidiscrete canonical Hamiltonian equations. Using symmetries, we find
conservation laws for the semidiscretized nonlinear wave equation and
Schrodinger equation.
