Letters in Mathematical Physics

, Volume 78, Issue 1, pp 27–37 | Cite as

From Integrable Lattices to Non-QRT Mappings

  • N. Joshi
  • B. Grammaticos
  • T. Tamizhmani
  • A. Ramani
Article

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.

Keywords

integrable mappings linearisation invariants reductions of lattice equations 

Mathematics Subject Classification (2000)

39A12 37J35 37J15 

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Copyright information

© Springer 2006

Authors and Affiliations

  • N. Joshi
    • 1
  • B. Grammaticos
    • 2
  • T. Tamizhmani
    • 2
    • 3
  • A. Ramani
    • 4
  1. 1.School of Mathematics and Statistics F07The University of SydneySydneyAustralia
  2. 2.GMPIBUniversité Paris VIIParisFrance
  3. 3.Department of MathematicsKanchi Mamunivar Centre for Postgraduate StudiesPondicherryIndia
  4. 4.CPTÉcole PolytechniquePalaiseauFrance

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