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Shabat Alexey Borisovich

Publications in Math-Net.Ru

  1. Darboux system and separation of variables in the Goursat problem for a third order equation in $\mathbb {R}^3$

    Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 4,  43–53
  2. Chebyshev polynomials, Catalan numbers, and tridiagonal matrices

    TMF, 204:1 (2020),  3–9
  3. Products of eigenfunctions and Wronskians

    Ufimsk. Mat. Zh., 12:2 (2020),  3–9
  4. Three theorems on Vandermond matrices

    Vladikavkaz. Mat. Zh., 22:1 (2020),  5–12
  5. Some exact solutions of the Volterra lattice

    TMF, 201:1 (2019),  37–53
  6. Conservation laws for Volterra chain with initial step-like condition

    Ufimsk. Mat. Zh., 11:1 (2019),  61–67
  7. Darboux system as three-dimensional analog of Liouville equation

    Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 12,  60–69
  8. Volterra chain and Catalan numbers

    Pis'ma v Zh. Èksper. Teoret. Fiz., 108:12 (2018),  834–837
  9. Darboux system: Liouville reduction and an explicit solution

    Trudy Mat. Inst. Steklova, 302 (2018),  268–286
  10. Cartan matrices in the Toda–Darboux chain theory

    TMF, 196:1 (2018),  22–29
  11. Constructive scattering theory

    TMF, 193:1 (2017),  15–24
  12. Some properties of Jost functions for Schrödinger equation with distribution potential

    Ufimsk. Mat. Zh., 9:4 (2017),  60–73
  13. On applications of Faà-di-Bruno formula

    Ufimsk. Mat. Zh., 9:3 (2017),  132–137
  14. Rational solutions of a Riccati equation

    Uspekhi Mat. Nauk, 71:4(430) (2016),  189–190
  15. Functional Cantor equation

    TMF, 189:3 (2016),  355–361
  16. Darboux transformations in the inverse scattering problem

    Ufimsk. Mat. Zh., 8:4 (2016),  43–52
  17. Inverse spectral problem for delta potentials

    Pis'ma v Zh. Èksper. Teoret. Fiz., 102:9 (2015),  705–708
  18. Difference Schrödinger equation and quasisymmetric polynomials

    TMF, 184:2 (2015),  200–211
  19. Scattering theory for delta-type potentials

    TMF, 183:1 (2015),  105–119
  20. Rational interpolation and solitons

    TMF, 179:3 (2014),  303–316
  21. Asymptotic behavior of generalized eigenvalues of the Schrödinger operator

    Vladikavkaz. Mat. Zh., 16:4 (2014),  9–15
  22. Periodic solutions of the Hopf equation

    TMF, 177:2 (2013),  222–230
  23. Two-sided Darboux transformations

    TMF, 173:2 (2012),  207–218
  24. Quantum tops as examples of commuting differential operators

    TMF, 172:3 (2012),  355–374
  25. Differential operators commuting in the principal part

    TMF, 171:1 (2012),  18–25
  26. Characteristic Lie rings and integrable models in mathematical physics

    Ufimsk. Mat. Zh., 4:3 (2012),  17–85
  27. Symmetrical polynomials and conservation laws

    Vladikavkaz. Mat. Zh., 14:4 (2012),  83–94
  28. Theorem on commutation in the principal part

    Ufimsk. Mat. Zh., 3:4 (2011),  3–7
  29. Commuting differential operators in two-dimension

    Ufimsk. Mat. Zh., 3:2 (2011),  91–98
  30. Commuting differential operators

    TMF, 162:3 (2010),  334–344
  31. The structure of polynomial conservation laws

    TMF, 161:3 (2009),  318–326
  32. A nonlinear eigenvalue problem

    TMF, 157:2 (2008),  175–187
  33. Model equation of the theory of solitons

    TMF, 153:1 (2007),  29–45
  34. On the One Class of Hyperbolic Systems

    SIGMA, 2 (2006), 093, 17 pp.
  35. Dressing chain for the acoustic spectral problem

    TMF, 149:1 (2006),  32–46
  36. Elementary Darboux Transformations and Factorization

    TMF, 144:1 (2005),  143–152
  37. Hydrodynamic Reductions and Solutions of a Universal Hierarchy

    TMF, 140:2 (2004),  216–229
  38. Universal Models of Soliton Hierarchies

    TMF, 136:2 (2003),  197–208
  39. Lagrangian Chains and Canonical Bäcklund Transformations

    TMF, 129:2 (2001),  163–183
  40. Symmetry approach to the integrability problem

    TMF, 125:3 (2000),  355–424
  41. Third version of the dressing method

    TMF, 121:1 (1999),  165–176
  42. Integrable lattices

    TMF, 118:2 (1999),  217–228
  43. First integrals of generalized Toda chains

    TMF, 115:3 (1998),  349–357
  44. Generalized Legendre transformations

    TMF, 112:2 (1997),  179–194
  45. On the one class of the Toda chains

    TMF, 111:3 (1997),  323–334
  46. Boundary value problem for the KdV equation on a half-line

    TMF, 110:1 (1997),  98–113
  47. Factorization and Poisson correspondences

    TMF, 105:2 (1995),  225–245
  48. On the Laplace–Darboux theory of transformations

    TMF, 103:1 (1995),  170–175
  49. Construction of reflectionless potentials with infinite discrete spectrum

    TMF, 100:2 (1994),  230–247
  50. Discrete symmetries and solitons

    TMF, 99:3 (1994),  537–544
  51. Dressing Chains and Spectral Theory of the Schrödinger Operator

    Funktsional. Anal. i Prilozhen., 27:2 (1993),  1–21
  52. Symmetries of nonlinear lattices

    Algebra i Analiz, 2:2 (1990),  183–208
  53. The use of computer algebra to investigate the integrability of nonlinear evolution systems

    Zh. Vychisl. Mat. Mat. Fiz., 28:11 (1988),  1674–1684
  54. On an extension of the module of invertible transformations

    Dokl. Akad. Nauk SSSR, 295:2 (1987),  288–291
  55. The symmetry approach to the classification of non-linear equations. Complete lists of integrable systems

    Uspekhi Mat. Nauk, 42:4(256) (1987),  3–53
  56. Integrability conditions for systems of two equations of the form $u_t=A(u)u_{xx}+F(u,u_x)$. II

    TMF, 66:1 (1986),  47–65
  57. Integrability conditions for systems of two equations of the form $u_t+A(u)u_{xx}+F(u,u_x)$. I

    TMF, 62:2 (1985),  163–185
  58. Systems of equations $u_x=p(u,\,v)$, $v_y=q(u,\,v)$ that possess symmetries

    Dokl. Akad. Nauk SSSR, 277:1 (1984),  29–33
  59. The group of internal symmetries and the conditions of integrability of two-dimensional dynamical systems

    TMF, 51:1 (1982),  10–21
  60. Infinite Lie–Beklund algebras

    Funktsional. Anal. i Prilozhen., 14:4 (1980),  79–80
  61. $(L,A)$-Pairs and a Ricatti type substitution

    Funktsional. Anal. i Prilozhen., 14:2 (1980),  79–80
  62. Evolutionary equations with nontrivial Lie–Bäcklund group

    Funktsional. Anal. i Prilozhen., 14:1 (1980),  25–36
  63. Equations of Liouville type

    Dokl. Akad. Nauk SSSR, 249:1 (1979),  26–29
  64. The Klein–Gordon equation with nontrivial group

    Dokl. Akad. Nauk SSSR, 247:5 (1979),  1103–1107
  65. Korteweg–de Vries equation from the group standpoint

    Dokl. Akad. Nauk SSSR, 244:1 (1979),  57–61
  66. An inverse scattering problem

    Differ. Uravn., 15:10 (1979),  1824–1834
  67. Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II

    Funktsional. Anal. i Prilozhen., 13:3 (1979),  13–22
  68. Inverse-scattering problem for a system of differential equations

    Funktsional. Anal. i Prilozhen., 9:3 (1975),  75–78
  69. A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I

    Funktsional. Anal. i Prilozhen., 8:3 (1974),  43–53
  70. On the Korteweg–de Vries equation

    Dokl. Akad. Nauk SSSR, 211:6 (1973),  1310–1313
  71. On a class of equations of Wiener-Hopf type

    Dokl. Akad. Nauk SSSR, 205:3 (1972),  546–549
  72. A one-dimensional scattering theory. I

    Differ. Uravn., 8:1 (1972),  164–178
  73. A generalized Fourier transform and asymptotic behavior of the solutions of the telegrapher's equation

    Differ. Uravn., 7:1 (1971),  157–165
  74. The Cauchy problem for the nonlinear Schrödinger equation

    Differ. Uravn., 6:1 (1970),  137–146
  75. An analog of the Rado–Cartan theorem for solutions of elliptic equations

    Dokl. Akad. Nauk SSSR, 166:6 (1966),  1304–1307
  76. On a property of solutions of elliptic equations of second order

    Dokl. Akad. Nauk SSSR, 163:2 (1965),  303–305
  77. The removability of level sets for solutions to elliptic equations

    Dokl. Akad. Nauk SSSR, 160:5 (1965),  1032–1035
  78. On two pasting problems

    Dokl. Akad. Nauk SSSR, 150:6 (1963),  1242–1245
  79. Математические вопросы гидродинамики жидкости со свободными границами

    Prikl. Mekh. Tekh. Fiz., 4:4 (1963),  3–16
  80. Об одной схеме плоского движения жидкости при наличии на дне траншеи

    Prikl. Mekh. Tekh. Fiz., 3:4 (1962),  68–80
  81. Boundary-value problems with small parameter for ordinary linear differential equations

    Uspekhi Mat. Nauk, 17:1(103) (1962),  235–241

  82. Vladimir Evgen'evich Zakharov (on his sixtieth birthday)

    UFN, 169:10 (1999),  1161–1162
  83. Ramil' Faritovich Bikbaev (obituary)

    Uspekhi Mat. Nauk, 51:1(307) (1996),  133–136

© Steklov Math. Inst. of RAS, 2025