Algebraic entropy, symmetries and linearization of quad equations consistent on the cube

Abstract

We discuss the non–autonomous nonlinear partial difference equations belonging to Boll classification of quad graph equations consistent around the cube. We show how starting from the compatible equations on a cell we can construct the lattice equations, its Bäcklund transformations and Lax pairs. By carrying out the algebraic entropy calculations we show that the H⁴ trapezoidal and the H⁶ families are linearizable and in a few examples we show how we can effectively linearize them.