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SIGMA, 2007, Volume 3, 080, 17 pages (Mi sigma206)  

This article is cited in 11 scientific papers (total in 11 papers)

Bäcklund Transformation for the BC-Type Toda Lattice

Vadim Kuznetsova, Evgeny Sklyaninb

a Deceased
b Department of Mathematics, University of York, York YO10 5DD, UK

Abstract: We study an integrable case of $n$-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a Bäcklund transformationand prove its basic properties: canonicity, commutativity and spectrality. The Bäcklund transformation can be also viewed as a discretized time dynamics. Two Lax matrices are used: of order 2 and of order $2n+2$, which are mutually dual, sharing the same spectral curve.

Keywords: Bäcklund transformation; Toda lattice; integrability; boundary conditions; classical Lie algebras

DOI: https://doi.org/10.3842/SIGMA.2007.080

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Full text: http://emis.mi.ras.ru/.../080
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ArXiv: 0707.1950
MSC: 70H06
Received: July 13, 2007; Published online July 25, 2007
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Citation: Vadim Kuznetsov, Evgeny Sklyanin, “Bäcklund Transformation for the BC-Type Toda Lattice”, SIGMA, 3 (2007), 080, 17 pp.

Citation in format AMSBIB
\Bibitem{KuzSkl07}
\by Vadim Kuznetsov, Evgeny Sklyanin
\paper B\"acklund Transformation for the BC-Type Toda Lattice
\jour SIGMA
\yr 2007
\vol 3
\papernumber 080
\totalpages 17
\mathnet{http://mi.mathnet.ru/sigma206}
\crossref{https://doi.org/10.3842/SIGMA.2007.080}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2366942}
\zmath{https://zbmath.org/?q=an:1157.70012}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000207065200080}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Igor V. Komarov, “Vadim Kuznetsov. Informal Biography by Eyes of His First Adviser”, SIGMA, 3 (2007), 074, 6 pp.  mathnet  crossref  mathscinet  zmath
    2. St. Petersburg Math. J., 22:3 (2011), 411–435  mathnet  crossref  mathscinet  zmath  isi
    3. Khanra B., Choudhury A.G., “On Backlund transformation of D-n type Toda lattice”, Phys Lett A, 374:40 (2010), 4120–4127  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. O. Ragnisco, F. Zullo, “Quantum Bäcklund transformations: Some ideas and examples”, Theoret. and Math. Phys., 172:2 (2012), 1160–1171  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    5. Pickering A., Zhu Z.-n., “Darboux–Bäcklund Transformation and Explicit Solutions To a Hybrid Lattice of the Relativistic Toda Lattice and the Modified Toda Lattice”, Phys. Lett. A, 378:21 (2014), 1510–1513  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Vakhnenko O.O., “Nonlinear Integrable Model of Frenkel-Like Excitations on a Ribbon of Triangular Lattice”, J. Math. Phys., 56:3 (2015), 033505  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Vakhnenko O.O., “Integrable Nonlinear Schrodinger System on a Triangular-Lattice Ribbon”, J. Phys. Soc. Jpn., 84:1 (2015), 014003  crossref  adsnasa  isi  scopus
    8. Zhang N., Xia T., “a Hierarchy of Lattice Soliton Equations Associated With a New Discrete Eigenvalue Problem and Darboux Transformations”, Int. J. Nonlinear Sci. Numer. Simul., 16:7-8 (2015), 301–306  crossref  mathscinet  isi  elib  scopus
    9. Vakhnenko O.O., “Semi-Discrete Integrable Nonlinear Schrodinger System With Background-Controlled Inter-Site Resonant Coupling”, J. Nonlinear Math. Phys., 24:2 (2017), 250–302  crossref  mathscinet  isi  scopus
    10. Avan J., Caudrelier V., Crampe N., “From Hamiltonian to Zero Curvature Formulation For Classical Integrable Boundary Conditions”, J. Phys. A-Math. Theor., 51:30 (2018), 30LT01  crossref  isi  scopus
    11. Zubkov M.Yu., “Application of Experimental Tectonic Methods in Petroleum Geology on the Examples of Deposits in Western Siberia”, Geotectonics, 53:3 (2019), 383–398  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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