From Integrable Lattices to Non-QRT Mappings |
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| Authors: | N Joshi B Grammaticos T Tamizhmani A Ramani |
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| Institution: | (1) School of Mathematics and Statistics F07, The University of Sydney, Sydney, NSW, 2006, Australia;(2) GMPIB, Université Paris VII, Tour 24-14, 5ème étage, case 7021, Paris, 75251, France;(3) Department of Mathematics, Kanchi Mamunivar Centre for Postgraduate Studies, Pondicherry, India;(4) CPT, école Polytechnique, CNRS, UMR 7644, Palaiseau, 91128, France |
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| Abstract: | Second-order mappings obtained as reductions of integrable lattice equations are generally expected to have integrals that are ratios of biquadratic polynomials, i.e., to be of QRT-type. In this paper we find reductions of integrable lattice equations that are not of this type. The mappings we consider are exact reductions of integrable lattice equations proposed by Adler et al. Comm Math Phys 233: 513, 2003]. Surprisingly, we found that these mappings possess invariants that are of the type originally studied by Hirota et al. J Phys A 34: 10377, 2001]. Moreover, we show that several mappings obtained are linearisable and we present their linearisation. |
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| Keywords: | integrable mappings linearisation invariants reductions of lattice equations |
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