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Journal of Nonlinear Mathematical Physics Volume 15, 2008 - Issue sup3: Nonlinear Evolution Equations and Dynamical Systems 2007
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Original Articles

Solutions of Adler’s Lattice Equation Associated with 2-Cycles of the Bäcklund Transformation

James Atkinson Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK E-mail: [email protected]@maths.leeds.ac.uk
&
Frank Nijhoff Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK E-mail: [email protected]@maths.leeds.ac.uk
Pages 34-42 | Published online: 21 Jan 2013

References

  • Weiss , J . 1986 . Periodic fixed points of Bäcklund transformations and the Korteweg-de Vries equation . J. Math. Phys. , 27 : 2647 – 2656 .
  • Weiss , J . 1987 . Periodic fixed points of Bäcklund transformations . J. Math. Phys. , 28 : 2025 – 2039 .
  • Atkinson , J , Hietarinta , J and Nijhoff , F . 2007 . Seed and soliton solutions for Adler’s lattice equation . J. Phys A , 40 : F1 – F8 .
  • Adler , V E . 1998 . Bäcklund Transformation For The Krichever-Novikov Equation . Intl. Math. Res. Notices , 1 : 1 – 4 .
  • Krichever , I M and Novikov , S P . 1979 . Holomorphic Fiberings and Nonlinear Equations . Sov. Math. Dokl. , 20 : 650 – 654 .
  • Krichever , I M and Novikov , S P . 1980 . Holomorphic Bundles over Algebraic Curves and Nonlinear Equations . Russ. Math. Surv. , 35 : 53 – 79 .
  • Nijhoff , F W and Walker , A J . 2001 . The Discrete and Continuous Painlevé VI Hierarchy and the Garnier Systems . Glasgow Math. J. , 43A : 109 – 123 .
  • Bobenko , A I and Suris , Yu B . 2002 . Integrable systems on quad-graphs . Intl. Math. Res. Notices , 11 : 573 – 611 .
  • Nijhoff , F W . 2002 . Lax pair for the Adler (lattice Krichever-Novikov) system . Phys. Lett. A , 297 : 49 – 58 .
  • Papageorgiou , V G , Nijhoff , F W and Capel , H W . 1990 . Integrable mappings and nonlinear integrable lattice equations . Phys. Lett. A , 147 : 106 – 114 .
  • Capel , H W , Nijhoff , F W and Papageorgiou , V G . 1991 . Complete integrability of Lagrangian mappings and lattices of KdV type . Phys. Lett. A , 155 : 377 – 387 .
  • Veselov , A P . 1991 . Integrable maps . Russ. Math. Surv. , 46 ( 5 ) : 1 – 51 .
  • Joshi , N , Grammaticos , B , Tamizhmani , T and Ramani , A . 2006 . From Integrable Lattices to Non-QRT Mappings . Lett. Math. Phy. , 78 ( 1 ) : 27 – 37 .
  • Nijhoff , F W and Enolskii , V Z . 1999 . “ Integrable Mappings of KdV type and hyperelliptic addition theorems ” . In Symmetries and integrability of Difference Equations , Edited by: Clarkson , P A and Nijhoff , F W . 64 – 78 . Cambridge Univ. Press .
  • Hietarinta , J . 2005 . Searching For CAC-maps . J. Nonlinear Math. Phys. , 12 ( 2 ) : 223 – 230 .

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