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TMF, 2000, Volume 122, Number 2, Pages 251–271 (Mi tmf567)  

This article is cited in 12 scientific papers (total in 12 papers)

Graded Lie algebras, representation theory, integrable mappings, and integrable systems

A. N. Leznovab

a Institute for High Energy Physics
b National Autonomous University of Mexico, Institute of Applied Mathematics and Systems

Abstract: A new class of integrable mappings and chains is introduced. The corresponding $1+2$ integrable systems that are invariant under such integrable mappings are presented in an explicit form. Soliton-type solutions of these systems are constructed in terms of matrix elements of fundamental representations of semisimple $A_n$ algebras for a given group element. The possibility of generalizing this construction to the multidimensional case is discussed.


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English version:
Theoretical and Mathematical Physics, 2000, 122:2, 211–228

Bibliographic databases:

Citation: A. N. Leznov, “Graded Lie algebras, representation theory, integrable mappings, and integrable systems”, TMF, 122:2 (2000), 251–271; Theoret. and Math. Phys., 122:2 (2000), 211–228

Citation in format AMSBIB
\by A.~N.~Leznov
\paper Graded Lie algebras, representation theory, integrable mappings, and integrable systems
\jour TMF
\yr 2000
\vol 122
\issue 2
\pages 251--271
\jour Theoret. and Math. Phys.
\yr 2000
\vol 122
\issue 2
\pages 211--228

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    This publication is cited in the following articles:
    1. Hu, XB, “Application of Hirota's bilinear formalism to a two-dimensional lattice by Leznov”, Physics Letters A, 276:1–4 (2000), 65  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. A. N. Leznov, “Discrete Symmetries of the $n$-Wave Problem”, Theoret. and Math. Phys., 132:1 (2002), 955–969  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Maruno, K, “Bilinear forms of integrable lattices related to Toda and Lotka-Volterra lattices”, Journal of Nonlinear Mathematical Physics, 9 (2002), 127  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. Tam, HW, “A generalized Leznov lattice: Bilinear form, Backlund transformation, and Lax pair”, Applied Mathematics Letters, 17:1 (2004), 35  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. J. Zhao, X. Hu, H. Tam, “Applying the Pfaffianization Procedure to the Two-Dimensional Leznov Lattice”, Theoret. and Math. Phys., 144:3 (2005), 1288–1295  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Wang, HY, “On the two-dimensional Leznov lattice equation with self-consistent sources”, Journal of Physics A-Mathematical and Theoretical, 40:42 (2007), 12691  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. Yu, GF, “On the integrable discrete versions of the Leznov lattice: Determinant solutions and Pfaffianization”, Journal of Mathematical Analysis and Applications, 335:1 (2007), 377  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    8. Leznov, AN, “Resolving of discrete transformation chains and multisoliton solution of the 3-wave problem”, Journal of Nonlinear Mathematical Physics, 14:2 (2007), 238  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Li, CX, “COMMUTATIVITY OF PFAFFIANIZATION AND BACKLUND TRANSFORMATIONS: THE LEZNOV LATTICE”, Journal of Nonlinear Mathematical Physics, 16:2 (2009), 169  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    10. Hu, XB, “Integrable semi-discretizations and full-discretization of the two-dimensional Leznov lattice”, Journal of Difference Equations and Applications, 15:3 (2009), 233  crossref  mathscinet  isi  scopus  scopus  scopus
    11. Hu J., Yu G.-F., Tam H.-W., “Commutativity of the Source Generation Procedure and Integrable Semi-Discretizations: the Two-Dimensional Leznov Lattice”, J. Phys. A-Math. Theor., 45:14 (2012), 145208  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    12. Qin B., Tian B., Wang Yu.-F., Shen Yu.-J., Wang M., “Bell-Polynomial Approach and Wronskian Determinant Solutions For Three Sets of Differential-Difference Nonlinear Evolution Equations With Symbolic Computation”, Z. Angew. Math. Phys., 68:5 (2017), 111  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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