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TMF, 2012, Volume 173, Number 3, Pages 363–374 (Mi tmf8350)  

This article is cited in 9 scientific papers (total in 9 papers)

An integrable multicomponent quad-equation and its Lagrangian formulation

J. Atkinsona, S. B. Lobbb, F. W. Nijhoffc

a University of Sydney, Sydney, Australia
b La Trobe University, Melbourne, Australia
c University of Leeds, Leeds, UK

Abstract: We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg–de Vries equation and the lattice modified Boussinesq equation. The $N$th member in the hierarchy is an $N$-component system defined on an elementary plaquette in the two-dimensional lattice. The system is multidimensionally consistent, and we obtain a Lagrangian that respects this feature, i.e., has the desirable closure property.

Keywords: integrable system, discrete equation, reduction, Lagrange formulation, variational principle

DOI: https://doi.org/10.4213/tmf8350

Full text: PDF file (440 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 173:3, 1644–1653

Bibliographic databases:

Received: 25.04.2012

Citation: J. Atkinson, S. B. Lobb, F. W. Nijhoff, “An integrable multicomponent quad-equation and its Lagrangian formulation”, TMF, 173:3 (2012), 363–374; Theoret. and Math. Phys., 173:3 (2012), 1644–1653

Citation in format AMSBIB
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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. F. Calogero, F. Leyvraz, “New solvable discrete-time many-body problem featuring several arbitrary parameters”, J. Math. Phys., 53:8 (2012), 082702, 19 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. R. Boll, M. Petrera, Yu. B. Suris, “Multi-time Lagrangian 1-forms for families of Bäcklund transformations: Toda-type systems”, J. Phys. A-Math. Theor., 46:27 (2013), 275204  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. Doliwa, “Non-commutative lattice-modified Gel'fand-Dikii systems”, J. Phys. A-Math. Theor., 46:20 (2013), 205202  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. I. T. Habibullin, M. N. Poptsova, “Asymptotic diagonalization of the discrete Lax pair around singularities and conservation laws for dynamical systems”, J. Phys. A-Math. Theor., 48:11 (2015), 115203  crossref  mathscinet  zmath  adsnasa  isi
    5. R. Boll, M. Petrera, Yu. B. Suris, “Multi-time Lagrangian 1-forms for families of Bäcklund transformations: relativistic Toda-type systems”, J. Phys. A-Math. Theor., 48:8 (2015), 085203  crossref  mathscinet  zmath  adsnasa  isi
    6. J. Hietarinta, N. Joshi, F. Nijhoff, Discrete systems and integrability, Cambridge Texts in Applied Mathematics, Cambridge University Press, 2016, xiii+445 pp.  mathscinet  zmath  isi
    7. A. P. Fordy, P. Xenitidis, “${{\mathbb{Z}}_{N}}$ graded discrete Lax pairs and integrable difference equations”, J. Phys. A-Math. Theor., 50:16 (2017), 165205  crossref  mathscinet  zmath  isi  scopus
    8. Ying Shi, Jonathan Nimmo, Junxiao Zhao, “Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation”, SIGMA, 13 (2017), 036, 18 pp.  mathnet  crossref
    9. M. Petrera, Yu. B. Suris, “Variational symmetries and pluri-Lagrangian systems in classical mechanics”, J. Nonlinear Math. Phys., 24:1, SI (2017), 121–145  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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