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TMF, 2000, Volume 125, Number 3, Pages 355–424 (Mi tmf675)  

This article is cited in 98 scientific papers (total in 98 papers)

Symmetry approach to the integrability problem

V. E. Adlera, A. B. Shabatb, R. I. Yamilova

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: We review the results of the twenty-year development of the symmetry approach to classifying integrable models in mathematical physics. The generalized Toda chains and the related equations of the nonlinear Schrödinger type, discrete transformations, and hyperbolic systems are central in this approach. Moreover, we consider equations of the Painlevé type, master symmetries, and the problem of integrability criteria for $(2+1)$-dimensional models. We present the list of canonical forms for $(1+1)$-dimensional integrable systems. We elaborate the effective tests for integrability and the algorithms for reduction to the canonical form.

DOI: https://doi.org/10.4213/tmf675

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English version:
Theoretical and Mathematical Physics, 2000, 125:3, 1603–1661

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Received: 19.07.2000

Citation: V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, TMF, 125:3 (2000), 355–424; Theoret. and Math. Phys., 125:3 (2000), 1603–1661

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. V. G. Marikhin, “Coulomb Gas Representation for Rational Solutions of the Painlevé Equations”, Theoret. and Math. Phys., 127:2 (2001), 646–663  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Svinin, AK, “A class of integrable lattices and KP hierarchy”, Journal of Physics A-Mathematical and General, 34:48 (2001), 10559  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Levi, D, “On the integrability of a new discrete nonlinear Schrodinger equation”, Journal of Physics A-Mathematical and General, 34:41 (2001), L553  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. 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
    5. Meshkov, AG, “Integrable evolution equations on the N-dimensional sphere”, Communications in Mathematical Physics, 232:1 (2002), 1  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Svinin, AK, “Extension of the discrete KP hierarchy”, Journal of Physics A-Mathematical and General, 35:8 (2002), 2045  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Kudryashov, NA, “Fourth-order analogies to the Painlevé equations”, Journal of Physics A-Mathematical and General, 35:21 (2002), 4617  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. N. A. Kudryashov, “On the Fourth Painlevé Hierarchy”, Theoret. and Math. Phys., 134:1 (2003), 86–93  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. V. K. Mel'nikov, “Structure of Equations Solvable by the Inverse Scattering Transform for the Schrödinger Operator”, Theoret. and Math. Phys., 134:1 (2003), 94–106  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. N. A. Kudryashov, “Amalgamations of the Painlevé Equations”, Theoret. and Math. Phys., 137:3 (2003), 1703–1715  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. Willox, R, “Painlevé equations from Darboux chains: I. P-III-P-V”, Journal of Physics A-Mathematical and General, 36:42 (2003), 10615  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    12. Hickman, MS, “Computation of densities and fluxes of nonlinear differential-difference equations”, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 459:2039 (2003), 2705  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    13. Tam, HW, “A special integrable differential-difference equation and its related systems: Bilinear forms soliton solutions and Lax pairs”, Journal of the Physical Society of Japan, 72:2 (2003), 265  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    14. Sergyeyev, A, “A remark on nonlocal symmetries for the Calogero-Degasperis-Ibragimov-Shabat equation”, Journal of Nonlinear Mathematical Physics, 10:1 (2003), 78  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    15. Kudryashov, NA, “Amalgamations of the Painlevé equations”, Journal of Mathematical Physics, 44:12 (2003), 6160  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    16. 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
    17. A. G. Meshkov, V. V. Sokolov, “Classification of Integrable Divergent $N$-Component Evolution Systems”, Theoret. and Math. Phys., 139:2 (2004), 609–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. 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
    19. I. T. Habibullin, E. V. Gudkova, “Boundary Conditions for Multidimensional Integrable Equations”, Funct. Anal. Appl., 38:2 (2004), 138–148  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. Baldwin, D, “Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations”, Computer Physics Communications, 162:3 (2004), 203  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    21. Yamilov, R, “Integrability conditions for n and t dependent dynamical lattice equations”, Journal of Nonlinear Mathematical Physics, 11:1 (2004), 75  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    22. Anatoly G. Meshkov, Maxim Ju. Balakhnev, “Integrable Anisotropic Evolution Equations on a Sphere”, SIGMA, 1 (2005), 027, 11 pp.  mathnet  crossref  mathscinet  zmath
    23. Tsuchida, T, “Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I”, Journal of Physics A-Mathematical and General, 38:35 (2005), 7691  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    24. Hydon, PE, “Multisymplectic conservation laws for differential and differential-difference equations”, Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 461:2058 (2005), 1627  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    25. Hereman W., Sanders J.A., Sayers J., Wang J.P., “Symbolic computation of polynomial conserved densities, generalized symmetries, and recursion operators for nonlinear differential-difference equations”, Group Theory and Numerical Analysis, CRM Proceedings & Lecture Notes, 39, 2005, 133–148  crossref  mathscinet  zmath  isi
    26. A. G. Meshkov, “On symmetry classification of third order evolutionary systems of divergent type”, J. Math. Sci., 151:4 (2008), 3167–3181  mathnet  crossref  mathscinet  zmath
    27. M. D. Vereschagin, S. D. Vereschagin, A. V. Yurov, “Trekhmernoe preobrazovanie Mutara”, Matem. modelirovanie, 18:5 (2006), 111–125  mathnet  mathscinet  zmath
    28. Vsevolod E. Adler, Alexey B. Shabat, “On the One Class of Hyperbolic Systems”, SIGMA, 2 (2006), 093, 17 pp.  mathnet  crossref  mathscinet  zmath
    29. 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
    30. Levi, D, “Continuous symmetries of difference equations”, Journal of Physics A-Mathematical and General, 39:2 (2006), R1  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    31. Wang, Q, “New rational formal solutions for (1+1)-dimensional Toda equation and another Toda equation”, Chaos Solitons & Fractals, 29:4 (2006), 904  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    32. Svinin, AK, “Comment to: “Two hierarchies of lattice soliton equations associated with a new discrete eigenvalue problem and Darboux transformation””, Physics Letters A, 350:5–6 (2006), 419  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    33. 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
    34. M. V. Demina, N. A. Kudryashov, “Special polynomials and rational solutions of the hierarchy of the second Painlevé equation”, Theoret. and Math. Phys., 153:1 (2007), 1398–1406  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    35. Tam, HW, “(2+1)-dimensional integrable lattice hierarchies related to discrete fourth-order nonisospectral problems”, Journal of Physics A-Mathematical and Theoretical, 40:43 (2007), 13031  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    36. Novikov, VS, “Symmetry structure of integrable nonevolutionary equations”, Studies in Applied Mathematics, 119:4 (2007), 393  crossref  mathscinet  isi  scopus  scopus
    37. Yu, YX, “Rational formal solutions of differential-difference equations”, Chaos Solitons & Fractals, 33:5 (2007), 1642  crossref  mathscinet  adsnasa  isi  scopus  scopus
    38. Xie, FD, “Some solutions of discrete sine-Gordon equation”, Chaos Solitons & Fractals, 33:5 (2007), 1791  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    39. Yu, YX, “Rational formal solutions of hybrid lattice equation”, Applied Mathematics and Computation, 186:1 (2007), 474  crossref  mathscinet  zmath  isi  scopus  scopus
    40. Hereman, W, “Continuous and discrete homotopy operators: A theoretical approach made concrete”, Mathematics and Computers in Simulation, 74:4–5 (2007), 352  crossref  mathscinet  zmath  isi  scopus  scopus
    41. B. I. Suleimanov, ““Quantizations” of the second Painlevé equation and the problem of the equivalence of its $L$$A$ pairs”, Theoret. and Math. Phys., 156:3 (2008), 1280–1291  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    42. V. V. Zharinov, “Evolution systems on a lattice”, Theoret. and Math. Phys., 157:3 (2008), 1694–1706  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    43. Kudryashov, NA, “The generalized Yablonskii-Vorob'ev polynomials and their properties”, Physics Letters A, 372:29 (2008), 4885  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    44. Demskoi, DK, “On recursion operators for elliptic models”, Nonlinearity, 21:6 (2008), 1253  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    45. 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
    46. 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
    47. JETP Letters, 88:3 (2008), 164–166  mathnet  crossref  isi  elib
    48. Xu, XX, “A 2-parameter hierarchy of integrable lattice equations”, Modern Physics Letters B, 22:14 (2008), 1389  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    49. JETP Letters, 87:5 (2008), 266–270  mathnet  crossref  isi  elib
    50. V. M. Zhuravlev, “The method of generalized Cole–Hopf substitutions and new examples of linearizable nonlinear evolution equations”, Theoret. and Math. Phys., 158:1 (2009), 48–60  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    51. Hao Hong-hai, Zhang Da-jun, Deng Shu-fang, “The Kadomtsev–Petviashvili equation with self-consistent sources in nonuniform media”, Theoret. and Math. Phys., 158:2 (2009), 151–166  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    52. V. V. Zharinov, “Green's formula for difference operators”, Theoret. and Math. Phys., 161:2 (2009), 1445–1450  mathnet  crossref  crossref  mathscinet  zmath  isi
    53. Levi, D, “The generalized symmetry method for discrete equations”, Journal of Physics A-Mathematical and Theoretical, 42:45 (2009), 454012  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    54. Huang, WH, “Jacobi elliptic function solutions of the Ablowitz-Ladik discrete nonlinear Schrodinger system”, Chaos Solitons & Fractals, 40:2 (2009), 786  crossref  zmath  adsnasa  isi  scopus  scopus
    55. V. V. Zharinov, “A differential-difference bicomplex”, Theoret. and Math. Phys., 165:2 (2010), 1401–1420  mathnet  crossref  crossref  isi
    56. Levi D., Winternitz P., Yamilov R.I., “Lie point symmetries of differential-difference equations”, J. Phys. A: Math. Theor., 43:29 (2010), 292002  crossref  mathscinet  zmath  isi  scopus  scopus
    57. Gordoa P.R., Pickering A., Zhu Z.-N., “Matrix semidiscrete Ablowitz-Ladik equation hierarchy and a matrix discrete second Painlevé equation”, J Math Phys, 51:5 (2010), 053505  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    58. Zhuravlev V.M., Zinov'ev D.A., “The application of generalized Cole-Hopf substitutions in compressible-fluid hydrodynamics”, Physics of Wave Phenomena, 18:4 (2010), 245–250  crossref  isi  scopus  scopus
    59. A. V. Mikhailov, J. P. Wang, P. Xenitidis, “Recursion operators, conservation laws, and integrability conditions for difference equations”, Theoret. and Math. Phys., 167:1 (2011), 421–443  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    60. Balakhnev M.J., “New examples of the auto-Backlund transformations and nonlinear superposition formulas for vector evolution systems”, Phys Lett A, 375:3 (2011), 529–536  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    61. V. S. Gerdjikov, G. G. Grahovski, A. V. Mikhailov, T. I. Valchev, “Rational bundles and recursion operators for integrable equations on A.III-type symmetric spaces”, Theoret. and Math. Phys., 167:3 (2011), 740–750  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    62. V. V. Zharinov, “Symmetries and conservation laws of difference equations”, Theoret. and Math. Phys., 168:2 (2011), 1019–1034  mathnet  crossref  crossref  mathscinet  adsnasa  elib  elib
    63. Vladimir S. Gerdjikov, Georgi G. Grahovski, Alexander V. Mikhailov, Tihomir I. Valchev, “Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces”, SIGMA, 7 (2011), 096, 48 pp.  mathnet  crossref  mathscinet
    64. Decio Levi, Pavel Winternitz, Ravil I. Yamilov, “Symmetries of the Continuous and Discrete Krichever–Novikov Equation”, SIGMA, 7 (2011), 097, 16 pp.  mathnet  crossref  mathscinet
    65. Xenitidis P., “Symmetries and conservation laws of the ABS equations and corresponding differential-difference equations of Volterra type”, J. Phys. A: Math. Theor., 44:43 (2011), 435201  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    66. Mikhailov A.V., Wang J.P., Xenitidis P., “Cosymmetries and Nijenhuis recursion operators for difference equations”, Nonlinearity, 24:7 (2011), 2079–2097  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    67. Tsuchida T., “Systematic method of generating new integrable systems via inverse Miura maps”, J Math Phys, 52:5 (2011), 053503  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    68. Balakhnev M.J., “The Vector Ito-Drienfel'd-Sokolov System: Bilinear Backlund Transformation and Lax pair”, J Phys Soc Japan, 80:4 (2011), 045002  crossref  adsnasa  isi  elib  scopus  scopus
    69. Levi D., Yamilov R.I., “Generalized symmetry integrability test for discrete equations on the square lattice”, J. Phys. A: Math. Theor., 44:14 (2011), 145207  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    70. B. I. Suleimanov, ““Kvantovaya” linearizatsiya uravnenii Penleve kak komponenta ikh $L,A$ par”, Ufimsk. matem. zhurn., 4:2 (2012), 127–135  mathnet
    71. A. V. Zhiber, R. D. Murtazina, I. T. Khabibullin, A. B. Shabat, “Kharakteristicheskie koltsa Li i integriruemye modeli matematicheskoi fiziki”, Ufimsk. matem. zhurn., 4:3 (2012), 17–85  mathnet  mathscinet
    72. Demskoi D.K., Viallet C.-M., “Algebraic Entropy for Semi-Discrete Equations”, J. Phys. A-Math. Theor., 45:35 (2012), 352001  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    73. Tsuda T., “From KP/Uc Hierarchies to Painlevé Equations”, Int. J. Math., 23:5 (2012), 1250010  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    74. Garifullin R.N., Yamilov R.I., “Generalized Symmetry Classification of Discrete Equations of a Class Depending on Twelve Parameters”, J. Phys. A-Math. Theor., 45:34 (2012), 345205  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    75. 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
    76. Ferapontov E.V., Novikov V.S., Roustemoglou I., “Towards the Classification of Integrable Differential-Difference Equations in 2+1 Dimensions”, J. Phys. A-Math. Theor., 46:24 (2013), 245207  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    77. 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
    78. Scimiterna Ch., Hay M., Levi D., “On the Integrability of a New Lattice Equation Found By Multiple Scale Analysis”, J. Phys. A-Math. Theor., 47:26 (2014), 265204  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    79. Demskoi D.K., “Quad-Equations and Auto-Backlund Transformations of NLS-Type Systems”, J. Phys. A-Math. Theor., 47:16 (2014), 165204  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    80. A. B. Shabat, “Scattering theory for delta-type potentials”, Theoret. and Math. Phys., 183:1 (2015), 540–552  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    81. J. P. Wang, “Representations of $\mathfrak{sl}(2,\mathbb{C})$ in category $\mathcal O$ and master symmetries”, Theoret. and Math. Phys., 184:2 (2015), 1078–1105  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    82. Adler V.E., “Integrability Test For Evolutionary Lattice Equations of Higher Order”, J. Symbolic Comput., 74 (2016), 125–139  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    83. Arnaudon A., “On a Lagrangian Reduction and a Deformation of Completely Integrable Systems”, J. Nonlinear Sci., 26:5 (2016), 1133–1160  crossref  mathscinet  zmath  isi  elib  scopus
    84. Garifullin R.N. Yamilov R.I. Levi D., “Non-invertible transformations of differential–difference equations”, J. Phys. A-Math. Theor., 49:37 (2016), 37LT01  crossref  mathscinet  zmath  isi  elib  scopus
    85. Talati D., Turhan R., “Two-component integrable generalizations of Burgers equations with nondiagonal linearity”, J. Math. Phys., 57:4 (2016), 041502  crossref  mathscinet  zmath  isi  elib  scopus
    86. Garifullin R.N. Yamilov R.I. Levi D., “Classification of five-point differential-difference equations”, J. Phys. A-Math. Theor., 50:12 (2017), 125201  crossref  mathscinet  zmath  isi  scopus
    87. Talati D., Wazwaz A.-M., “Some new integrable systems of two-component fifth-order equations”, Nonlinear Dyn., 87:2 (2017), 1111–1120  crossref  mathscinet  zmath  isi  scopus
    88. Ismagil Habibullin, Mariya Poptsova, “Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings”, SIGMA, 13 (2017), 073, 26 pp.  mathnet  crossref
    89. Gubbiotti G., Scimiterna C., Levi D., “The Non-Autonomous Ydkn Equation and Generalized Symmetries of Boll Equations”, J. Math. Phys., 58:5 (2017), 053507  crossref  mathscinet  zmath  isi  scopus  scopus
    90. Tian K., Wang J.P., “Symbolic Representation and Classification of N=1 Supersymmetric Evolutionary Equations”, Stud. Appl. Math., 138:4 (2017), 467–498  crossref  mathscinet  zmath  isi  scopus
    91. Talati D., Wazwaz A.-M., “Some Classification of Non-Commutative Integrable Systems”, Nonlinear Dyn., 88:2 (2017), 1487–1492  crossref  mathscinet  isi  scopus  scopus
    92. Garifullin R.N. Yamilov R.I. Levi D., “Classification of Five-Point Differential-Difference Equations II”, J. Phys. A-Math. Theor., 51:6 (2018), 065204  crossref  mathscinet  zmath  isi  scopus  scopus
    93. Sergyeyev A., “New Integrable (3+1)-Dimensional Systems and Contact Geometry”, Lett. Math. Phys., 108:2 (2018), 359–376  crossref  mathscinet  zmath  isi  scopus  scopus
    94. Perepelkin E.E., Sadovnikov B.I., Inozemtseva N.G., “Solutions of Nonlinear Equations of Divergence Type in Domains Having Corner Points”, J. Elliptic Parabol. Equat., 4:1 (2018), 107–139  crossref  mathscinet  zmath  isi
    95. M. N. Poptsova, I. T. Habibullin, “Algebraic properties of quasilinear two-dimensional lattices connected with integrability”, Ufa Math. J., 10:3 (2018), 86–105  mathnet  crossref  isi
    96. M. N. Poptsova, “Simmetrii odnoi periodicheskoi tsepochki”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 80–84  mathnet
    97. Gubbiotti G., “Algebraic Entropy of a Class of Five-Point Differential-Difference Equations”, Symmetry-Basel, 11:3 (2019), 432  crossref  isi
    98. Perepelkin E.E., Kovalenko A.D., Tarelkin A.A., Polyakova R.V., Sadovnikov B.I., Inozemtseva N.G., Sysoev P.N., Sadovnikova M.B., “Simulation of Magnetic Systems in the Domain With a Corner”, Phys. Part. Nuclei, 50:3 (2019), 341–394  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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