New Integrable and Linearizable Nonlinear Difference Equations

A systematic investigation to derive nonlinear lattice equations governed by partial difference (P??E) admitting specific Lax representation is presented. Further it shown that for a value of the parameter derived P??E's can be transformed into linear under global transformation. Also demonstrated how higher order ordinary (O?E) or mappings in general and linearizable ones particular from obtained through periodic reduction. The question measure preserving property O?E's construction more than one integrals (or invariants) them examined wherever possible.