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TMF, 2000, Volume 124, Number 1, Pages 48–61 (Mi tmf625)  

This article is cited in 19 scientific papers (total in 19 papers)

Discretizations of the Landau–Lifshits equation

V. E. Adler

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

Abstract: The relation between the Sklyanin chain and the Bдcklund transformations for the Landau–Lifshits equation is established. The stationary solutions of the chain determine an integrable mapping, which is a kind of classical Heisenberg spin chain. Some multifield generalizations are found.


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English version:
Theoretical and Mathematical Physics, 2000, 124:1, 897–908

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Received: 31.01.2000

Citation: V. E. Adler, “Discretizations of the Landau–Lifshits equation”, TMF, 124:1 (2000), 48–61; Theoret. and Math. Phys., 124:1 (2000), 897–908

Citation in format AMSBIB
\by V.~E.~Adler
\paper Discretizations of the Landau--Lifshits equation
\jour TMF
\yr 2000
\vol 124
\issue 1
\pages 48--61
\jour Theoret. and Math. Phys.
\yr 2000
\vol 124
\issue 1
\pages 897--908

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    This publication is cited in the following articles:
    1. V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, Theoret. and Math. Phys., 125:3 (2000), 1603–1661  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Calogero, F, “A novel solvable many-body problem with elliptic interactions”, International Mathematics Research Notices, 2000, no. 15, 775  crossref  mathscinet  zmath  isi
    3. V. E. Adler, V. G. Marikhin, A. B. Shabat, “Lagrangian Chains and Canonical Bäcklund Transformations”, Theoret. and Math. Phys., 129:2 (2001), 1448–1465  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Suris, YB, “Integrable discretizations of some cases of the rigid body dynamics”, Journal of Nonlinear Mathematical Physics, 8:4 (2001), 534  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Suris, YB, “Integrability of Adler's discretization of the Neumann system”, Physics Letters A, 279:5–6 (2001), 327  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Nijhoff, FW, “Lax pair for the Adler (lattice Krichever-Novikov) system”, Physics Letters A, 297:1–2 (2002), 49  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. R. I. Yamilov, “Relativistic Toda Chains and Schlesinger Transformations”, Theoret. and Math. Phys., 139:2 (2004), 623–635  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    8. Adler, VE, “Q(4): Integrable master equation related to an elliptic curve”, International Mathematics Research Notices, 2004, no. 47, 2523  crossref  mathscinet  zmath  isi
    9. Suris Y.B., “Discrete Lagrangian models”, Discrete Integrable Systems, Lecture Notes in Physics, 644, 2004, 111–184  crossref  mathscinet  zmath  adsnasa  isi
    10. Vsevolod E. Adler, Alexey B. Shabat, “On the One Class of Hyperbolic Systems”, SIGMA, 2 (2006), 093, 17 pp.  mathnet  crossref  mathscinet  zmath
    11. 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  scopus
    12. Adler, VE, “Classification of integrable Volterra-type lattices on the sphere: isotropic case”, Journal of Physics A-Mathematical and Theoretical, 41:14 (2008), 145201  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    13. F. Khanizadeh, A. V. Mikhailov, Jing Ping Wang, “Darboux transformations and recursion operators for differential–difference equations”, Theoret. and Math. Phys., 177:3 (2013), 1606–1654  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. Jennings P., Nijhoff F., “On an Elliptic Extension of the Kadomtsev-Petviashvili Equation”, J. Phys. A-Math. Theor., 47:5 (2014), 055205  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    15. Delice N., Nijhoff F.W., Yoo-Kong S., “On Elliptic Lax Systems on the Lattice and a Compound Theorem For Hyperdeterminants”, J. Phys. A-Math. Theor., 48:3 (2015), 035206  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    16. V. G. Marikhin, “Action as an invariant of Bäcklund transformations for Lagrangian systems”, Theoret. and Math. Phys., 184:1 (2015), 953–960  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    17. Suris Yu.B., “Discrete Time Toda Systems”, J. Phys. A-Math. Theor., 51:33 (2018)  crossref  mathscinet  isi
    18. Nijhoff F., Delice N., “On Elliptic Lax Pairs and Isomonodromic Deformation Systems For Elliptic Lattice Equations in Honour of Professor Noumi For the Occasion of His 60Th Birthday”, Representation Theory, Special Functions and Painleve Equations - Rims 2015, Advanced Studies in Pure Mathematics, 76, eds. Konno H., Sakai H., Shiraishi J., Suzuki T., Yamada Y., Math Soc Japan, 2018, 487–525  mathscinet  isi
    19. Zhao P., Fan E., Temuerchaolu, “Quasiperiodic Solutions of the Heisenberg Ferromagnet Hierarchy”, J. Nonlinear Math. Phys., 26:3 (2019), 468–482  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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