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arxiv: 1603.07930 · v1 · pith:M3HD4Z2Inew · submitted 2016-03-25 · 🌊 nlin.SI · math-ph· math.MP

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

classification 🌊 nlin.SI math-phmath.MP
keywords equationsalgebraicconsistentcubeentropyquadacklundaround
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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 B\"acklund transformations and Lax pairs. By carrying out the algebraic entropy calculations we show that the $H^4$ trapezoidal and the $H^6$ families are linearizable and in a few examples we show how we can effectively linearize them.

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