Variational discrete symmetries

The invertible differential substitutions that conserve the standard Poisson brackets and act on Hamiltonians in an appropriate way are considered. These canonical auto-Baecklund transformations proved to be a very simple and efficient tool in the theory of solitons. In particular, these allow one to prove a general involutivity theorem and to build up simple formulae for soliton-like solutions of (2+1)-dimensional Hamiltonian systems as well as in (1+1)-dimensional case. 7 refs