  The article studies a class of integrable semidiscrete equations with one
continuous and two discrete independent variables. Miura type transformations
are obtained that relate the equations of the class. A new integrable chain of
this type is found, for which the Lax pair is presented. Integrable in the
sense of Darboux reductions of the chain are discussed, for small order
reductions complete sets of integrals are constructed. Continuum limits for the
chain are discussed. A method for finding particular solutions of chains based
on integrable in sense of Darboux reductions is proposed. The effectiveness of
the method is illustrated by an example.
