Аннотация:
Formal diagonalisation of Lax operators leads to formal diagonalisation of
the corresponding Darboux transformations. The latter enables us to find
recurrent relations for generating conservation laws and establish natural
relations between the canonical series of local conservation laws for
partial differential equations (PDEs), differential-difference equations ( PD
$\Delta $Es) and partial difference equations (P$\Delta $Es), PD$\Delta $Es
and P$\Delta $Es. In particular we show that the canonical densities of
conservation laws for the symmetries of P$\Delta $Es are canonical densities
of the partial difference equations themselves.