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TMF, 1997, Volume 111, Number 3, Pages 323–334 (Mi tmf1011)  

This article is cited in 23 scientific papers (total in 23 papers)

On the one class of the Toda chains

V. E. Adlera, A. B. Shabatb

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: The main result of our paper is the list of integrable generalizations of the Toda lattice. Apart from known lattices this list contains three new examples. Each lattice from the list gives the Bäcklund transformation for some NLS type system.


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English version:
Theoretical and Mathematical Physics, 1997, 111:3, 647–657

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Received: 04.03.1997

Citation: V. E. Adler, A. B. Shabat, “On the one class of the Toda chains”, TMF, 111:3 (1997), 323–334; Theoret. and Math. Phys., 111:3 (1997), 647–657

Citation in format AMSBIB
\by V.~E.~Adler, A.~B.~Shabat
\paper On the one class of the Toda chains
\jour TMF
\yr 1997
\vol 111
\issue 3
\pages 323--334
\jour Theoret. and Math. Phys.
\yr 1997
\vol 111
\issue 3
\pages 647--657

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    This publication is cited in the following articles:
    1. V. E. Adler, A. B. Shabat, “Generalized Legendre transformations”, Theoret. and Math. Phys., 112:2 (1997), 935–948  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Marikhin, VG, “Hamiltonian theory of integrable generalizations of the nonlinear Schrodinger equation”, JETP Letters, 66:11 (1997), 705  crossref  adsnasa  isi  scopus  scopus  scopus
    3. V. E. Adler, A. B. Shabat, “First integrals of generalized Toda chains”, Theoret. and Math. Phys., 115:3 (1998), 639–646  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Zhuravlev, VM, “Diffusive Toda chains in models of nonlinear waves in active media”, Journal of Experimental and Theoretical Physics, 87:5 (1998), 1031  crossref  adsnasa  isi  scopus  scopus  scopus
    5. Adler, VE, “Backlund transformation for the Krichever-Novikov equation”, International Mathematics Research Notices, 1998, no. 1, 1  crossref  mathscinet  isi
    6. A. B. Shabat, “Third version of the dressing method”, Theoret. and Math. Phys., 121:1 (1999), 1397–1408  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Marikhin V.G., Shabat A.B., “Hamiltonian theory of Backlund transformations”, Optical Solitons: Theoretical Challenges and Industrial Perspectives, Centre de Physique Des Houches, no. 12, 1999, 19–29  isi
    8. 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
    9. A. K. Svinin, “Integrable Chains and Hierarchies of Differential Evolution Equations”, Theoret. and Math. Phys., 130:1 (2002), 11–24  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Cieslinski, JL, “Darboux covariant equations of von Neumann type and their generalizations”, Journal of Mathematical Physics, 44:4 (2003), 1763  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    11. 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
    12. Adler, VE, “Q(4): Integrable master equation related to an elliptic curve”, International Mathematics Research Notices, 2004, no. 47, 2523  crossref  mathscinet  zmath  isi
    13. Ustinov, NV, “The lattice equations of the Toda type with an interaction between a few neighbourhoods”, Journal of Physics A-Mathematical and General, 37:5 (2004), 1737  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    14. Suris Y.B., “Discrete Lagrangian models”, Discrete Integrable Systems, Lecture Notes in Physics, 644, 2004, 111–184  crossref  mathscinet  zmath  adsnasa  isi
    15. Vsevolod E. Adler, Alexey B. Shabat, “On the One Class of Hyperbolic Systems”, SIGMA, 2 (2006), 093, 17 pp.  mathnet  crossref  mathscinet  zmath
    16. 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  scopus
    17. R. I. Yamilov, “Integrability conditions for an analogue of the relativistic Toda chain”, Theoret. and Math. Phys., 151:1 (2007), 492–504  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. Chen Ya., Ismail M.E.H., “Hypergeometric Origins of Diophantine Properties Associated with the Askey Scheme”, Proceedings of the American Mathematical Society, 138:3 (2010), 943–951  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    19. Boll R., Petrera M., Suris Yu.B., “Multi-Time Lagrangian 1-Forms For Families of Backlund Transformations. Relativistic Toda-Type Systems”, J. Phys. A-Math. Theor., 48:8 (2015), 085203  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    20. V. G. Marikhin, “Three-dimensional lattice of Bäcklund transformations of integrable cases of the Davey–Stewartson system”, Theoret. and Math. Phys., 189:3 (2016), 1718–1725  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    21. Zhang Yu. Zhou R.-G., “A Chain of Type II and Its Exact Solutions”, Chin. Phys. Lett., 33:11 (2016), 110203  crossref  isi  scopus
    22. Aminov G., Mironov A., Morozov A., “Modular Properties of 6D (Dell) Systems”, J. High Energy Phys., 2017, no. 11, 023  crossref  mathscinet  isi  scopus  scopus  scopus
    23. Suris Yu.B., “Discrete Time Toda Systems”, J. Phys. A-Math. Theor., 51:33 (2018)  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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