  Inspired by the forms of delay-Painleve equations, we consider some new
differential-discrete systems of KdV, mKdV and Sine-Gordon - type related by
simple one way Miura transformations to classical ones. Using Hirota bilinear
formalism we construct their new integrable discretizations, some of them
having higher order. In particular, by this procedure, we show that the
integrable discretization of intermediate sine-Gordon equation is exactly
lattice mKdV and also we find a bilinear form of the recently proposed lattice
Tzitzeica equation. Also the travelling wave reduction of these new lattice
equations is studied and it is shown that all of them, including the higher
order ones, can be integrated to Quispel-Roberts-Thomson (QRT) mappings.
