On conservation properties of semidiscrete canonical Hamiltonian equations

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 [11]. The same result holds for semidiscrete Hamiltonian equations [7]. In this paper we briefly review semidiscrete canonical Hamiltonian equations, considered in [8] in greater details. Using symmetries, we find conservation laws for the semidiscretized nonlinear wave equation.