New Integrable and Linearizable Nonlinear Difference Equations

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