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A G and Tran D T Towards some exact results for the (vanishing) algebraic entropy of (integrable) lattice equations in preparation (0)

by J Roberts
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A Lax pair of a lattice equation whose entropy vanishes

by Dinh T. Tran , 2014
"... In this paper, we present multi parametric quadgraph equations which are consistent around the cube. These equations are obtained by applying a ‘double twist ’ to known integrable equations. Furthermore, we perform a limit to one of these equations to derive the non-symmetric equation which is Equat ..."
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In this paper, we present multi parametric quadgraph equations which are consistent around the cube. These equations are obtained by applying a ‘double twist ’ to known integrable equations. Furthermore, we perform a limit to one of these equations to derive the non-symmetric equation which is Equation 19 in [7]. As a result, we obtain a novel Lax pair of this equation. 1
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...sed as a simple integrability test 1 ar X iv :1 41 0. 65 28 v1s[ nli n.S I]s23sO cts20 14 for a decade. However, it has only been proven recently for certain lattice equations subject to a conjecture =-=[12]-=-. On the other hand, ‘low complexity‘ has been used in [7] to search for integrable lattice equations on a square. The authors searched for multi-affine equations on a quad-graph with a certain factor...

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