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Journal of Nonlinear Mathematical Physics Volume 12, 2005 - Issue sup2: Symmetries and Integrability of Difference Equations SIDE VI
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Original Articles

Bilinear recurrences and addition formulae for hyperelliptic sigma functions

Harry W Braden School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Kings Buildings, Mayfield Road, EH9 3JZ, Edinburgh, U.K. E-mail: [email protected]
,
Victor Z Enolskii Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, UK E-mail: [email protected]
&
Andrew N W Hone Institute of Mathematics and Statistics, University of Kent, CT2 7NF, Canterbury, U.K. E-mail: [email protected]
Pages 46-62 | Published online: 21 Jan 2013

Citations (12)

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Read on this site (1)

Andrew N.W. Hone. (2010) Analytic solutions and integrability for bilinear recurrences of order six. Applicable Analysis 89:4, pages 473-492.
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Articles from other publishers (11)

Andrew N. W. Hone. (2020) Continued Fractions and Hankel Determinants from Hyperelliptic Curves. Communications on Pure and Applied Mathematics 74:11, pages 2310-2347.
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Fumitaka Yura. (2015) Hankel determinant solution for elliptic sequence. Linear Algebra and its Applications 484, pages 27-45.
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Yuri N. Fedorov & Andrew N. W. Hone. (2015) Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties. Journal of Integrable Systems 1:1, pages xyw012.
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Xiang-Ke Chang & Xing-Biao Hu. (2012) A conjecture based on Somos-4 sequence and its extension. Linear Algebra and its Applications 436:11, pages 4285-4295.
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V.Z. Enolski, E. Hackmann, V. Kagramanova, J. Kunz & C. Lämmerzahl. (2011) Inversion of hyperelliptic integrals of arbitrary genus with application to particle motion in general relativity. Journal of Geometry and Physics 61:5, pages 899-921.
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N. A. Kostov, V. S. Gerdjikov & V. Mioc. (2010) Exact solutions for a class of integrable Hénon–Heiles-type systems. Journal of Mathematical Physics 51:2.
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E. Yu. Bunkova & V. M. Buchstaber. (2009) Heat equations and families of two-dimensional sigma functions. Proceedings of the Steklov Institute of Mathematics 266:1, pages 1-28.
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Shigeki Matsutani & Emma Previato. (2009) A generalized Kiepert formula for C ab curves. Israel Journal of Mathematics 171:1, pages 305-323.
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ANDREW N. W. HONE & CHRISTINE SWART. (2008) Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences. Mathematical Proceedings of the Cambridge Philosophical Society 145:1, pages 65-85.
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A. Hone. (2007) Sigma function solution of the initial value problem for Somos 5 sequences. Transactions of the American Mathematical Society 359:10, pages 5019-5034.
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A.N.W. Hone. (2007) Singularity confinement for maps with the Laurent property. Physics Letters A 361:4-5, pages 341-345.
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