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Algebra i Analiz, 1990, Volume 2, Issue 2, Pages 183–208 (Mi aa180)  

This article is cited in 33 scientific papers (total in 33 papers)

Research Papers

Symmetries of nonlinear lattices

A. B. Shabat, R. I. Yamilov

Institute of Mathematics of Bashkirian Scientific Centre, UB of USSR Academy of Sciences

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English version:
Leningrad Mathematical Journal, 1991, 2:2, 377–400

Bibliographic databases:

Received: 14.06.1989

Citation: A. B. Shabat, R. I. Yamilov, “Symmetries of nonlinear lattices”, Algebra i Analiz, 2:2 (1990), 183–208; Leningrad Math. J., 2:2 (1991), 377–400

Citation in format AMSBIB
\by A.~B.~Shabat, R.~I.~Yamilov
\paper Symmetries of nonlinear lattices
\jour Algebra i Analiz
\yr 1990
\vol 2
\issue 2
\pages 183--208
\jour Leningrad Math. J.
\yr 1991
\vol 2
\issue 2
\pages 377--400

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    This publication is cited in the following articles:
    1. R. I. Yamilov, “Invertible changes of variables generated by Bäcklund transformations”, Theoret. and Math. Phys., 85:2 (1990), 1269–1275  mathnet  crossref  mathscinet  zmath  isi
    2. A. P. Veselov, “Integrable maps”, Russian Math. Surveys, 46:5 (1991), 1–51  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. P. Veselov, A. B. Shabat, “Dressing Chains and Spectral Theory of the Schrödinger Operator”, Funct. Anal. Appl., 27:2 (1993), 81–96  mathnet  crossref  mathscinet  zmath  isi
    4. V. E. Adler, “Recuttings of Polygons”, Funct. Anal. Appl., 27:2 (1993), 141–143  mathnet  crossref  mathscinet  zmath  isi
    5. S. I. Svinolupov, R. I. Yamilov, “Explicit Bäcklund transformations for multifield Schrödinger equations. Jordan generalizations of the Toda chain”, Theoret. and Math. Phys., 98:2 (1994), 139–146  mathnet  crossref  mathscinet  zmath  isi
    6. A. B. Shabat, “Discrete symmetries and solitons”, Theoret. and Math. Phys., 99:3 (1994), 783–789  mathnet  crossref  mathscinet  zmath  isi
    7. Theoret. and Math. Phys., 99:2 (1994), 635–640  mathnet  crossref  mathscinet  zmath  isi
    8. E. V. Ferapontov, “Laplace transformations of hydrodynamic-type systems in Riemann invariants”, Theoret. and Math. Phys., 110:1 (1997), 68–77  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. V. E. Adler, A. B. Shabat, “On the one class of the Toda chains”, Theoret. and Math. Phys., 111:3 (1997), 647–657  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. 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
    11. V. E. Adler, I. T. Habibullin, “Boundary Conditions for Integrable Lattices”, Funct. Anal. Appl., 31:2 (1997), 75–85  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. 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
    13. S. Ya. Startsev, “Differential substitutions of the Miura transformation type”, Theoret. and Math. Phys., 116:3 (1998), 1001–1010  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. A. B. Shabat, “Third version of the dressing method”, Theoret. and Math. Phys., 121:1 (1999), 1397–1408  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. V. E. Adler, “Discretizations of the Landau–Lifshits equation”, Theoret. and Math. Phys., 124:1 (2000), 897–908  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. 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
    17. A. B. Borisov, “Bcklund Transformation and Dressing Chains for the Landau–Lifshitz Equation”, Theoret. and Math. Phys., 128:2 (2001), 1025–1033  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. 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
    19. 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
    20. S. V. Smirnov, “Cyclic $q$-chains”, St. Petersburg Math. J., 15:5 (2004), 795–811  mathnet  crossref  mathscinet  zmath
    21. T. G. Kazakova, “Finite-Dimensional Discrete Systems Integrated in Quadratures”, Theoret. and Math. Phys., 138:3 (2004), 356–369  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. 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
    23. V. E. Adler, A. B. Shabat, “Dressing chain for the acoustic spectral problem”, Theoret. and Math. Phys., 149:1 (2006), 1324–1337  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    24. Vsevolod E. Adler, Alexey B. Shabat, “On the One Class of Hyperbolic Systems”, SIGMA, 2 (2006), 093, 17 pp.  mathnet  crossref  mathscinet  zmath
    25. A. G. Meshkov, “Nonlocal symmetries in two-field divergent evolutionary systems”, Theoret. and Math. Phys., 156:3 (2008), 1268–1279  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    26. Decio Levi, Matteo Petrera, Christian Scimiterna, Ravil Yamilov, “On Miura Transformations and Volterra-Type Equations Associated with the Adler–Bobenko–Suris Equations”, SIGMA, 4 (2008), 077, 14 pp.  mathnet  crossref  mathscinet  zmath
    27. 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
    28. I. T. Habibullin, M. V. Yangubaeva, “Formal diagonalization of a discrete Lax operator and conservation laws and symmetries of dynamical systems”, Theoret. and Math. Phys., 177:3 (2013), 1655–1679  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    29. R. N. Garifullin, A. V. Mikhailov, R. I. Yamilov, “Discrete equation on a square lattice with a nonstandard structure of generalized symmetries”, Theoret. and Math. Phys., 180:1 (2014), 765–780  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    30. V. E. Adler, “Necessary integrability conditions for evolutionary lattice equations”, Theoret. and Math. Phys., 181:2 (2014), 1367–1382  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    31. 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
    32. Charalampos A. Evripidou, Peter H. van der Kamp, Cheng Zhang, “Dressing the Dressing Chain”, SIGMA, 14 (2018), 059, 14 pp.  mathnet  crossref
    33. G. S. Mauleshova, “The dressing chain and one-point commuting difference operators of rank 1”, Siberian Math. J., 59:5 (2018), 901–908  mathnet  crossref  crossref  isi
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