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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 1, Pages 1–11 (Mi faa278)  

This article is cited in 16 scientific papers (total in 16 papers)

Legendre Transforms on a Triangular Lattice

V. E. Adler

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: We show that the condition of invariance with respect to generalized Legendre transforms effectively singles out a class of integrable difference equations on a triangular lattice; these equations are discrete analogs of relativistic Toda lattices. Some of these equations are apparently new. For one of them, higher symmetries are written out and the zero curvature representation is obtained.


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English version:
Functional Analysis and Its Applications, 2000, 34:1, 1–9

Bibliographic databases:

UDC: 517.962.24
Received: 21.08.1998

Citation: V. E. Adler, “Legendre Transforms on a Triangular Lattice”, Funktsional. Anal. i Prilozhen., 34:1 (2000), 1–11; Funct. Anal. Appl., 34:1 (2000), 1–9

Citation in format AMSBIB
\by V.~E.~Adler
\paper Legendre Transforms on a Triangular Lattice
\jour Funktsional. Anal. i Prilozhen.
\yr 2000
\vol 34
\issue 1
\pages 1--11
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 1
\pages 1--9

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    This publication is cited in the following articles:
    1. Adler, VE, “Discrete equations on planar graphs”, Journal of Physics A-Mathematical and General, 34:48 (2001), 10453  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Bobenko, AI, “Integrable systems on quad-graphs”, International Mathematics Research Notices, 2002, no. 11, 573  crossref  mathscinet  zmath  isi
    3. Bobenko, AI, “Hexagonal circle patterns and integrable systems: Patterns with the multi-ratio property and lax equations on the regular triangular lattice”, International Mathematics Research Notices, 2002, no. 3, 111  crossref  mathscinet  zmath  isi
    4. Bobenko, AI, “Hexagonal circle patterns and integrable systems: Patterns with constant angles”, Duke Mathematical Journal, 116:3 (2003), 525  crossref  mathscinet  zmath  isi  scopus
    5. Adler, VE, “Q(4): Integrable master equation related to an elliptic curve”, International Mathematics Research Notices, 2004, no. 47, 2523  crossref  mathscinet  zmath  isi
    6. Suris Y.B., “Discrete Lagrangian models”, Discrete Integrable Systems, Lecture Notes in Physics, 644, 2004, 111–184  crossref  mathscinet  zmath  adsnasa  isi
    7. Yamilov, R, “Symmetries as integrability criteria for differential difference equations”, Journal of Physics A-Mathematical and General, 39:45 (2006), R541  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Doliwa, A, “Integrable lattices and their sublattices. II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices”, Journal of Mathematical Physics, 48:11 (2007), 113506  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Boll R., Suris Yu.B., “Non-symmetric discrete Toda systems from quad-graphs”, Appl Anal, 89:4 (2010), 547–569  crossref  mathscinet  zmath  isi  elib  scopus
    10. Scimiterna C., Levi D., “Three-Point Partial Difference Equations Linearizable by Local and Nonlocal Transformations”, J. Phys. A-Math. Theor., 46:2 (2013), 025205  crossref  mathscinet  adsnasa  isi  elib  scopus
    11. Boll R., Petrera M., Suris Yu.B., “Multi-Time Lagrangian 1-Forms for Families of Backlund Transformations: Toda-Type Systems”, J. Phys. A-Math. Theor., 46:27 (2013), 275204  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Boll R., Petrera M., Suris Yu.B., “What Is Integrability of Discrete Variational Systems?”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 470:2162 (2014), 20130550  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. Vekslerchik V.E., “Explicit solutions for a nonlinear model on the honeycomb and triangular lattices”, J. Nonlinear Math. Phys., 23:3 (2016), 399–422  crossref  mathscinet  isi  elib  scopus
    14. Lam W.Y., “Discrete Minimal Surfaces: Critical Points of the Area Functional From Integrable Systems”, Int. Math. Res. Notices, 2018, no. 6, 1808–1845  crossref  mathscinet  isi  scopus
    15. V. E. Adler, “Integrable seven-point discrete equations and second-order evolution chains”, Theoret. and Math. Phys., 195:1 (2018), 513–528  mathnet  crossref  crossref  adsnasa  isi  elib
    16. V. E. Vekslerchik, “Explicit Solutions for a Nonlinear Vector Model on the Triangular Lattice”, SIGMA, 15 (2019), 028, 17 pp.  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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