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Extension of the Adler-Bobenko-Suris classification of integrable lattice equations (0)

by Chris M Field
Venue:J. Phys. A: Math. Theor
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On non-multiaffine consistent-around-the-cube lattice equations

by Pavlos Kassotakis, Maciej Nieszporski , 2013
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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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... Sc = ( 1 c 0 1 ) , (17) and the following equation (x− y)(u− v) + (c1 + c2)(u− v) + (c1 − c2)(x− y) + c21 − c22 − p+ q = 0. (18) This equation is a slightly more general form of Equation B1 given in =-=[4]-=-. We have checked that this equation is consistent around the cube with lattice parameters ((p, c2), (q, c1)). Remark 3. We note that all the equations which we obtain in this sections can be transfor...

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