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Singularity Confinement Property for the (Non-Autonomous) Adler–Bobenko–Suris Integrable Lattice Equations

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Abstract

We examine the integrable lattice systems proposed by Adler, Bobenko and Suris from the point of view of the existence of integrable non-autonomous forms. We show, using the singularity confinement criterion, that both the H and Q families can be deautonomised, leading to a lattice with variable step in each dimension, as already assumed in the original paper. A new linearisable equation is identified as a special case of the Q4 lattice. We present its linearisation and obtain its non-autonomous extension.

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Authors and Affiliations

  1. IMNC, Université Paris VII-Paris XI, CNRS, UMR 8165, Bât. 104, 91406, Orsay, France

    Basil Grammaticos

  2. Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128, Palaiseau, France

    Alfred Ramani

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  1. Basil Grammaticos
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  2. Alfred Ramani
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Correspondence to Basil Grammaticos.

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Grammaticos, B., Ramani, A. Singularity Confinement Property for the (Non-Autonomous) Adler–Bobenko–Suris Integrable Lattice Equations. Lett Math Phys 92, 33–45 (2010). https://doi.org/10.1007/s11005-010-0378-4

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  • DOI: https://doi.org/10.1007/s11005-010-0378-4

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