Russian Academy of Sciences

Landau Institute for Theoretical Physics

Aleksei B. Shabat

Principal researcher

Doctor of science

Professor

Email:

Publications

    1. A.B. Shabat, Funktsional’noe uravnenie Kantora, TMF, 189(3), 355-361 (2016) [A.B. Shabat, Functional Cantor equation, Theor. Math. Phys., 189(3), 1712-1717 (2016)], WoS: 000392087200003, Scopus: 2-s2.0-85008711822.
    2. V.V. Sokolov, A.B. Shabat, O ratsional’nykh resheniyakh uravneniya Rikkati, UMN, 71:4(430), 189-190 (2016) [V.V. Sokolov, A.B. Shabat, Rational solutions of a Riccati equation, Russ. Math. Surveys, 71(4), 787–789 (2016)], Scopus: 2-s2.0-84997173251.
    3. M.Sh. Badakhov, A.B. Shabat, O preobrazovaniyakh Darbu v obratnoi zadache rasseyaniya, Ufimskii matem. zh., 8(4), 43-52 (2016) [M.S. Badakhov, A.B. Shabat, Darboux transformations in the inverse scattering problem, Ufa Math. J., 8(4), 42-51 (2016)], Scopus: 2-s2.0-85013379967.
    4. A.B. Shabat, R.Ch. Kulaev, Obratnaya zadacha rasseyaniya dlya finitnykh potentsialov v prostranstve mer Borelya, Preprint YuMI VNTs RAN, Vladikavkaz, №2 (2016) - 19 s.
    5. A.B. Shabat, Obratnaya spektral’naya zadacha dlya del’toobraznykh potentsialov, Pis’ma v ZhETF, 102 (9), 705-708 (2015) [A.B. Shabat, Inverse spectral problem for delta potentials, JETP Letters, 102(9), 620-623 (2015)], WoS: 000368691000010.
    6. A.B. Shabat, Teoriya rasseyaniya dlya del’taobraznykh potentsialov, TMF, 183(1), 105-119 (2015) [A.B. Shabat, Scattering theory for delta-type potentials, Theor. Math. Phys., 183(1), 540–552 (2015)], WoS: 000353242500007.
    7. A.B. Shabat, Raznostnoe uravnenie Shredingera i kvazisimmetricheskie mnogochleny, TMF, 184(2), 200-211 (2015) [A.B. Shabat, Difference Schrödinger equation and quasisymmetric polynomials, Theor. Math. Phys., 184(2), 1067-1077 (2015)], WoS: 000361532600002, Scopus: 2-s2.0-84942154609.
    8. A.B. Shabat, Vvedenie v teoriyu obratnoi zadachi rasseyani, V sbornike: Matematicheskii analiz i matematicheskoe modelirovanie. Trudy X regional’noi shkoly-konferentsii molodykh uchenykh "Vladikavkazskaya molodezhnaya matematicheskaya shkola", s. 101-110 (2015).
    9. M.Sh. Badakhov, O.Yu. Veremeenko, A.B. Shabat, Ob asimptotike obobshchennykh sobstvennykh znachenii operatora Shredingera, Vladikavk. matem. zhurn., 16(4), 9-15 (2014).
    10. A.B. Shabat, Ratsional’naya interpolyatsiya i solitony, TMF, 179(3), 303–316 (2014) [A.B. Shabat, Rational interpolation and solitons, Theor. Math. Phys., 179(3), 637–648 (2014)], WoS: 000338842800002, Scopus: 2-s2.0-84903850121.
    11. A.B. Shabat, Ob odnoi interpolyatsionnoi zadache, Matematicheskii forum (Itogi nauki. Yug Rossii), 8(2), 66-74 (2014) [Trudy Mezhdunarod. nauchn. konf. Poryadkovyi analiz i smezhnye voprosy matem. modelirovaniya, Vladikavkaz-N.Tsei, 14-20 iyulya 2013].
    12. A.B. Shabat, O periodicheskikh resheniyakh uravneniya Khopfa, TMF, 177(2), 222-230 (2013) [A.B. Shabat, Periodic solutions of the Hopf equation, Theor. Math. Phys., 177(2), 1471-1478 (2013)], WoS: 000328329300002, Scopus: 2-s2.0-84890084144.
    13. V.E. Adler, A.B. Shabat, Toward a theory of integrable hyperbolic equations of third order, J. Phys. A 45, 395207 (2012); arXiv:1206.4170, WoS: 000308912500011, Scopus: 2-s2.0-84866412321.
    14. A.B. Shabat, Simmetricheskie mnogochleny i zakony sokhraneniya, Vladikavkaz. matem. zhurn., 14(4), 83-94 (2012).
    15. R.A. Gabiev, A.B. Shabat, O differentsial’nykh operatorakh, kommutiruyushchikh v glavnom, TMF, 171(1), 18-25 (2012) [R.A. Gabiev, A.B. Shabat, Differential operators commuting in the principal part, Theor. Math. Phys., 171(1), 435-441 (2012)], WoS: 000303876200002, Scopus: 2-s2.0-84860631623.
    16. V.E. Adler, V.G. Marikhin, A.B. Shabat, Kvantovye volchki kak primery kommutiruyushchikh differentsial’nykh operatorov, TMF, 172(3), 355-374 (2012) [V.E. Adler, V.G. Marikhin, A.B. Shabat, Quantum tops as examples of commuting differential operators, Theor. Math. Phys., 172(3), 1187-1205 (2012)]; arXiv:1109.6770, WoS: 000309725400003, Scopus: 2-s2.0-84867434152.
    17. A.B. Shabat, Z.S. El’kanova, A.B. Urusova, Dvustoronnie preobrazovaniya Darbu, TMF, 173(2), 207–218 (2012) [A.B. Shabat, Z.S. Élkanova, A.B. Urusova, Two-sided Darboux transformations, Theor. Math. Phys., 173(2), 1507–1517 (2012)], WoS: 000312081200003, Scopus: 2-s2.0-84870734489.
    18. A.V. Zhiber, R.D. Murtazina, I.T. Khabibullin, A.B. Shabat, Kharakteristicheskie kol’tsa Li i integriruemye modeli matematicheskoi fiziki, Ufimsk. matem. zhurn., 4(3), 17-85 (2012).
    19. A.V. Zhiber, R.D. Murtazina, I.T. Khabibullin, A.B. Shabat, Kharakteristicheskie kol’tsa Li i nelineinye integriruemye uravneniya, Moskva-Izhevsk : In-t komp’yut. issled., 2012 g., 376 str. ISBN 978-5-4344-0092-3.
    20. A.B. Shabat, Z.S. El’kanova, O kommutiruyushchikh differentsial’nykh operatorakh v dvumerii, Ufimsk. matem. zhurn., 3(2), 91-99 (2011).
    21. M.S. Akbasheva, A.B. Shabat, Teorema o kommutirovanii v glavnom, Ufimsk. matem. zhurn., 3(4), 3-7 (2011).
    22. M.Kh. Chankaev, A.B. Shabat, Matematicheskii analiz v spektral’noi teorii, Ufa: BashkGU, 2011, 60 str.
    23. A. Shabat, E. Kartashova, Computable Integrability, arXiv:1103.2423.
    24. A.B. Shabat, Z.S. El’kanova, O kommutiruyushchikh differentsial’nykh operatorakh, TMF, 162(3), 334–344 (2010) [A.B. Shabat, Z.S. Elkanova, Commuting differential operators, Theor. Math. Phys., 162(3), 276–285 (2010)], Scopus: 2-s2.0-77952051600.
    25. R.N. Garifullin, A.B. Shabat, O strukture polinomial’nykh zakonov sokhraneniya, TMF, 161(3), 318–326 (2009) [R.N. Garifullin, A.B. Shabat, The structure of polynomial conservation laws, Theor. Math. Phys., 161(3), 1590–1598 (2009)], Scopus: 2-s2.0-76649144486.
    26. A. Shabat, Symmetries of Spectral Problems, Lect. Notes Phys., 767, 139-173 (2009) [Integrability, ed A.V. Mikhailov, Springer, xiii, 339 pp., ISBN 978-3-540-88110-0].
    27. M.Kh. Chankaev, A.B. Shabat, Ob odnoi nelineinoi zadache na sobstvennye znacheniya, TMF, 157(2), 175-187 (2008) [M.Kh. Chankaev, A.B. Shabat, A nonlinear eigenvalue problem, Theor. Math. Phys., 157(2), 1514–1524 (2008)].
    28. A.B. Shabat, Lektsii po teorii solitonov, KChGU, Karachaevsk, 2008, 60 str.
    29. V.E. Adler, A.B. Shabat, Model’noe uravnenie teorii solitonov, TMF, 153(1), 29-45 (2007) [V.E. Adler, A.B. Shabat, Model equation of the theory of solitons, Theor. Math. Phys., 153(1), 1373-1387 (2007)]; arXiv:0706.0075.
    30. A.B. Shabat, V.E. Adler, V.G. Marikhin, V.V. Sokolov (eds.), Encyclopedia of Integrable Systems, L.D. Landau Institute for Theoretical Physics - Research Institute for Symbolic Computations, J. Kepler Universität (2007) [on-line].
    31. V.E. Adler, A.B. Shabat, On the one class of hyperbolic systems, SIGMA, 2, 093 (2006); nlin/0612060.
    32. V.E. Adler, A.B. Shabat, Odevayushchaya tsepochka dlya akusticheskoi spektral’noi zadachi, TMF, 149(1), 32-46 (2006) [V.E. Adler, A.B. Shabat, Dressing chain for the acoustic spectral problem., Theor. Math. Phys., 149(1), 1324-1337 (2006)]; nlin/0604008.
    33. A. Shabat, Universal Solitonic Hierarchy, J. Nonlinear Math. Phys., 12, Suppl.1, 614-624 (2005).
    34. F. Musso, A.B. Shabat, Elementarnye preobrazovaniya Darbu i faktorizatsiya, TMF, 144(1), 143-152 (2005) [F. Musso, A.B. Shabat, Elementary Darboux transformations and factorization, Theor. Math. Phys., 144(1), 1004-1013 (2005)]; nlin/0502006.
    35. L.M. Alonso, A.B. Shabat, Gidrodinamicheskie reduktsii i resheniya universal’noi ierarkhii, TMF, 140(2), 216-229 (2004) [L.M. Alonso, A.B. Shabat, Hydrodynamic reductions and solutions of a universal hierarchy, Theor. Math. Phys., 140(2), 1073-1085 (2004)]; nlin/0312043.
    36. A.B. Shabat, A. González-López, M. Mañas, L. Martínez Alonso, M.A. Rodríguez (Eds.), New trends in integrability and partial solvability: Proc. of the NATO Advanced Research Workshop held at Cádiz University, Cádiz, June 13–15, 2002, NATO Science Series II: Mathematics, Physics and Chemistry, 132. Kluwer Academic Publishers, Dordrecht, 2004. xiv+297 pp. ISBN: 1-4020-1835-5.
    37. A.B. Shabat, L.M. Alonso, On the prolongation of a hierarchy of hydrodynamic chains, NATO Science Series II: Math. Phys. Chem., Vol.132, 263-280 (2004) [New Trends in Integrability and Partial Solvability: Proc. NATO ARW, Cádiz, June 13–15, 2002. Ed. by A.B. Shabat et al., Kluwer Academic Publishers, Dordrecht, 2004, xiv+297 pp. ISBN: 1-4020-1835-5].
    38. L.M. Alonso, A.B. Shabat, Towards a theory of differential constraints of a hydrodynamic hierarchy, J. Nonlinear Math. Phys., 10 (2), 229-242 (2003); nlin/0310036.
    39. R.H. Heredero, A. Shabat, V. Sokolov, A new class of linearizable equations, J. Phys. A 36(47), L605-L614 (2003); nlin/0301001.
    40. A.B. Shabat, Universal’nye modeli solitonnykh ierarkhii, TMF, 136(2), 197-208 (2003) [A.B. Shabat, Universal models of soliton hierarchies, Theor. Math. Phys., 136(2), 1066-1076 (2003)].
    41. A.B. Shabat, Discretization of the Schrodinger spectral problem, Inverse Problems, 18(4), 1003-1011 (2002).
    42. L.M. Alonso, A.B. Shabat, Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type, Phys. Lett. A 299 (4), 359-365 (2002); nlin/0202008.
    43. L.M. Alonso, A.B. Shabat, Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type, Phys. Lett. A 300 (1), 58-64 (2002).
    44. V.E. Adler, V.G. Marikhin, A.B. Shabat, Lagranzhevy tsepochki i kanonicheskie preobrazovaniya Beklunda, TMF, 129(2), 163-183 (2001) [V.E. Adler, V.G. Marikhin, A.B. Shabat, Lagrangian chains and canonical Backlund transformations, Theor. Math. Phys., 129(2), 1448-1465 (2001)].
    45. V.G. Marikhin, A.B Shabat, M. Boiti, F. Pempinelli, Avtomodel’nye resheniya tipa nelineinogo uravneniya Shredingera, ZhETF, 117(3), 634-643 (2000) [V.G. Marikhin, A.B. Shabat, M. Boiti, F. Pempinelli, Self-similar solutions of equations of the nonlinear Schrodinger type, JETP, 90(3), 553-561 (2000)].
    46. V.E. Adler, A.B. Shabat, R.I. Yamilov, Symmetry approach to the integrability problem, TMF, 125(3), 355-424 (2000) [V.E. Adler, A.B. Shabat, R.I. Yamilov, Symmetry approach to the integrability problem, Theor. Math. Phys., 125(3), 1603-1661 (2000)].
    47. A. Shabat, Dressing chains and lattices, Proc. Workshop on Nonlinearity, Integrability and All That: Twenty Years after NEEDS '79, Gallipoli, July 1–10, 1999, p. 331–342 (2000) [Edited by M. Boiti, L. Martina, F. Pempinelli, B. Prinari and G. Soliani. World Scientific Publishing Co., Inc., River Edge, NJ, 2000. xvi+550 pp. ISBN: 981-02-4147-X].
    48. V.G. Marikhin, A.B. Shabat, Integriruemye reshetki, TMF, 118(2), 217-228 (1999) [V.G. Marikhin, A.B. Shabat, Integrable lattices, Theor. Math. Phys., 118(2), 173-182 (1999)].
    49. A.B. Shabat, Tretii variant metoda odevaniya, TMF, 121(1), 165-176 (1999) [A.B. Shabat, Third version of the dressing method, Theor. Math. Phys., 121(1), 1397-1408 (1999)].
    50. V.G. Marikhin, A.B. Shabat, Hamiltonian theory of Bäcklund transformations, In: Optical Solitons: theoretical challenges and industrial perspectives, V.E. Zakharov, S. Wabnitz, editors, EDP Sciences, Les Ulis; Springer Verlag, Berlin, Heidelberg, 1999, pp. 19-29.
    51. M. Boiti, V.G. Marikhin, F. Pempinelli, A.B. Shabat, Self-similar solutions of NLS-type dynamical systems, solv-int/9909021.
    52. V.E. Adler, A.B. Shabat, Pervye integraly obobshchennykh tsepochek Tody, TMF, 115(3), 349-357 (1998) [V.E. Adler, A.B. Shabat, First integrals of generalized Toda chains, Theor. Math. Phys., 115(3), 639-646 (1998)].
    53. A.B. Shabat, R.I. Yamilov, To a transformation theory of two-dimensional integrable systems, Phys. Lett. A 227 (1-2), 15-23 (1997).
    54. V.E. Adler, I.T. Khabibullin, A.B. Shabat, Kraevaya zadacha dlya uravneniya KdF na poluosi, TMF, 110(1), 98-113 (1997) [V.E. Adler, I.T. Habibullin, A.B. Shabat, Boundary value problem for the KdV equation on a half-line, Theor. Math. Phys., 110(1), 78-90 (1997)].
    55. V.E. Adler, A.B. Shabat, Ob odnom klasse tsepochek Tody, TMF, 111(3), 323-334 (1997) [V.E. Adler, A.B. Shabat, On a class of Toda chains, Theor. Math. Phys., 111(3), 647-657 (1997)].
    56. V.E. Adler, A.B. Shabat, Obobshchennye preobrazovaniya Lezhandra, TMF, 112(2), 179-194 (1997) [V.E. Adler, A.B. Shabat, Generalized Legendre transformations, Theor. Math. Phys., 112(2), 935-948 (1997)].
    57. A.B. Shabat, First integrals of the infinite Toda lattice, CRM Proceedings and Lecture Notes, 9, 345-351 (1996) [Symmetries and Integrability of Difference Equations. Proc. workshop, Estérel, Quebec, May 22–29, 1994. Ed. by Decio Levi, Luc Vinet and Pavel Winternitz. AMS and CRM, 1996, xii+388 pp. ISBN: 0-8218-0601-7].
    58. A.I. Bobenko, A.M. Il’in, S.Yu. Dobrokhotov, A.R. Its, L.A. Kalyakin, V.B. Matveev, V.Yu. Novokshenov, A.B. Shabat, Ramil’ Faritovich Bikbaev (nekorolog), Uspekhi mat. nauk, 51:1(307), 133-136 (1996) [A.I. Bobenko, S.Yu. Dobrokhotov, A.M. Il’in, A.R. Its, L.A. Kalyakin, V.B. Matveev, V.Yu. Novokshenov, A.B. Shabat, Ramil' Faritovich Bikbaev (obituary), Russ. Math. Surv., 51(1), 129-133 (1996)].
    59. A.B. Shabat, Higher symmetries of two-dimensional lattices, Phys. Lett. A 200 (2), 121-133 (1995).
    60. A.B. Shabat, Toda chain and nonlinear Schrördinger equation. Nonlocalities, Physica D 87 (1-4), 1-8 (1995).
    61. A.B. Shabat, K teorii preobrazovanii Laplasa–Darbu, TMF, 103(1), 170-175 (1995) [A.B. Shabat, On the theory of Laplace-Darboux transformations, Theor. Math. Phys., 103(1), 482-485 (1995)].
    62. A.P. Fordy, A.B. Shabat, A.P. Veselov, Factorization and Poisson correspondences, TMF, 105(2), 225-245 (1995) [Theor. Math. Phys., 105(2), 1369-1386 (1995)].
    63. A. Shabat, The Kortteweg-de Vries Hierarchy, In: The first Landau Institute summer school, Moscow, Russia, July 4-25, 1993. Selected proceedings. Ed. by V.P. Mineev, London: Gordon and Breach Publishers, Lecture 7, 221-257 (1995). ISBN 2-88449-138-4.
    64. D. Levi, O. Ragnisco, A.B. Shabat, Construction of higher local (2 + 1) dimensional exponential lattice equations, Canad. J. Phys., 72(7-8), 439-441 (1994).
    65. A. Shabat, Discrete symmetries and solitons, TMF, 99(3), 537-544 (1994) [Theor. Math. Phys., 99(3), 783-789 (1994)].
    66. A. Degasperis, A. Shabat, Construction of reflectionless potentials with infinite discrete spectrum, TMF, 100(2), 230–247 (1994) [Theor. Math. Phys., 100(2), 970-984 (1994)].
    67. A.N. Leznov, A.B. Shabat, R.I. Yamilov, Canonical transformations generated by shifts in nonlinear lattices, Phys. Lett. A 174 (5-6), 397-402 (1993).
    68. A.P. Veselov, A.B. Shabat, Odevayushchaya tsepochka i spektral’naya teoriya operatora Shryodingera, Funkts. analiz i ego pril., 27(2), 1–21 (1993) [A.P. Veselov, A.B. Shabat, Dressing chains and the spectral theory of the Schrödinger operator, Funct. Anal. Appl., 27(2), 81-96 (1993)], WoS: A1993ME86400001.
    69. A.B. Shabat, A.V. Mikhailov, Symmetries — Test of integrability, In: Important developments in soliton theory. Springer Ser. Nonlinear Dyn., 355-374 (1993) [Ed. by A.S. Fokas et al., Berlin: Springer-Verlag, 1993. ISBN 3-540-55913-2].
    70. A. Degasperis, A. Shabat, Construction of reflectionless potentials with infinite discrete spectrum, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 413, 115-123 (1993) [Proc. NATO ARW «Applications of Analytical and Geometric Methods to Nonlinear Differential Equations», Exeter, July 14–19, 1992. Ed. by Peter A. Clarkson, Kluwer Academic Publishers Group, Dordrecht, 1993, x+477 pp. ISBN: 0-7923-2457-9].
    71. A. Shabat, The infinite-dimensional dressing dynamical system, Inverse Problems, 8(2), 303-308 (1992).
    72. A. Degasperis, A. Shabat, Construction of reflectionless potentials with infinitely many discrete eigenvalues, Preprint INFN ROME-919-1992. Dec 1992. 13 pp.
    73. A.N. Leznov, A.B. Shabat, R.I. Yamilov, Variational discrete symmetries, Preprint IFVE-92-143. okt. 1992, 20 s.
    74. A.V. Mikhailov, A.B. Shabat, V.V. Sokolov, The symmetry approach to classification of integrable equations, In: What is integrability?, Springer Ser. Nonlinear Dyn., 115-184 (1991) [Ed. by V.E. Zakharov, Berlin etc., Springer-Verlag, 1991. xiv, 321 pp. ISBN 3-540-51964-5].
    75. A.B. Shabat, R.I. Yamilov, Simmetrii nelineinykh tsepochek, Algebra i analiz, 2(2), 183–208 (1990) [A.B. Shabat, R.I. Yamilov, Symmetries of nonlinear chains, Leningr. Math. J., 2(2), 377–400 (1991)].
    76. A.V. Mikhailov, A.B. Shabat, V.V. Sokolov, Simmetriinyi podkhod k klassifikatsii integriruemykh uravnenii, V kn: “Integriruemost’ i kineticheskie uravneniya dlya solitonov”, Kiev: Naukova dumka, 1990, s.213-279.
    77. V.P. Gerdt, A.B. Shabat, S.I. Svinolupov, A.Yu. Zharkov, Computer algebra application for investigating integrability of nonlinear evolution systems, Lecture Notes in Comput. Sci., 378, 81-92 (1989) [Proc. EUROCAL '87. European Conference on Computer Algebra, Leipzig, GDR, June 2-5, 1987. Ed. by J.H. Davenport, Springer-Verlag, 1989, viii+499 pp].
    78. A.V. Mikhailov, A.B. Shabat, R.I. Yamilov, Extension of the module of invertible transformations. Classification of integrable systems, Commun. Math. Phys., 115 (1), 1-19 (1988).
    79. A.B. Shabat, R.I. Yamilov, Lattice representations of integrable systems, Phys. Lett. A 130(4-5), 271-275 (1988).
    80. V.P. Gerdt, A.Yu. Zharkov, S.I. Svinolupov, A.B. Shabat, Primenenie komp’yuternoi algebry dlya issledovaniya integriruemosti nelineinykh evolyutsionnykh sistem, Zh. vychisl. mat. i mat. fiz., 28(11), 1674-1684 (1988) [V.P. Gerdt, A.Yu. Zharkov, S.I. Svinolupov, A.B. Shabat, The use of computer algebra to investigate the integrability of non-linear evolution systems, USSR Comput. Math. & Math. Phys., 28(6), 50-57 (1988)].
    81. A.V. Mikhailov, A.B. Shabat, R.I. Yamilov, On an extension of the module of invertible transformations. (Russian), Dokl. Akad. nauk SSSR, 295 (2), 288-291 (1987) [A.V. Mikhailov, A.B. Shabat, R.I. Yamilov, On the extension of reversible transformation module, Sov. Math. Dokl. 36(1), 60-63 (1988)].
    82. A.V. Mikhailov, A.B. Shabat, R.I. Yamilov, Simmetriinyi podkhod k klassifikatsii nelineinykh uravnenii. Polnye spiski integriruemykh sistem, Uspekhi mat. nauk, 42:4(256), 3–53 (1987) [A.V. Mikhailov, A.B. Shabat, R.I. Yamilov, The symmetry approach to the classification of non-linear equations. Complete lists of integrable systems, Russ. Math. Surv., 42(4), 1-63 (1987)], WoS: A1987P639900001.
    83. A.V. Mikhailov, A.B. Shabat, Integrable deformations of the Heisenberg model, Phys. Lett. A 116 (4), 191-194 (1986).
    84. A.V. Mikhailov, A.B. Shabat, Usloviya integriruemosti sistem dvukh uravnenii tipa ut=A(u)uxx+F(u, ux). II, TMF, 66(1), 47-65 (1986) [A.V. Mikhailov, A.B. Shabat, Integrability conditions for systems of two equations of the form ut=A(u)uxx+F(u, ux). II, Theor. Math. Phys., 66(1), 31-44 (1986)].
    85. A.V. Mikhailov, A.B. Shabat, Usloviya integriruemosti sistem dvukh uravnenii tipa ut=A(u)uxx+F(u,ux). I, TMF, 62(2), 163-185 (1985) [A.V. Mikhailov, A.B. Shabat, Integrability conditions for systems of two equations of the form ut=A(u)uxx+F(u,ux). I, Theor. Math. Phys., 62(2), 107-122 (1985)].
    86. A.V. Zhiber, A.B. Shabat, Systems of equations ux=p(u,v), vy=q(u,v) that possess symmetries. (Russian), Dokl. Akad. nauk SSSR, 277(1), 29-33 (1965) [A.V. Zhiber, A.B. Shabat, Systems of equations ux=p(u,v), vy=q(u,v) that possess symmetries, Soviet Math. Dokl. 30(1), 23–26 (1984)].
    87. V.V. Sokolov, A.B. Shabat, Classification of integrable evolution equations, Sov. Sci. Rev., Sect. C, Math. Phys. Rev. 4, 221-280 (1984) [Edited by S. P. Novikov. Harwood Academic Publishers, Chur, 1984. ix+280 pp. ISBN: 3-7186-0146-X 58-06].
    88. A.N. Leznov, V.G. Smirnov, A.B. Shabat, Gruppa vnutrennikh simmetrii i usloviya integriruemosti dvumernykh dinamicheskikh sistem, TMF, 51(1), 10-21 (1982) [A.N. Leznov, V.G. Smirnov, A.B. Shabat, The group of internal symmetries and the conditions of integrability of two-dimensional dynamical systems, Theor. Math. Phys., 51(1), 322-330 (1982)].
    89. N.Kh. Ibragimov, A.B. Shabat, Evolyutsionnye uravneniya s netrivial’noi gruppoi Li–Beklunda, Funkts. analiz i ego pril., 14(1), 25-36 (1980) [N.Kh. Ibragimov, A.B. Shabat, Evolutionary equations with nontrivial Lie-Bäcklund group, Funct. Anal. Appl., 14(1), 19-28 (1980)].
    90. V.V. Sokolov, A.B. Shabat, L,A-pary i zamena tipa Rikatti, Funkts. analiz i ego pril., 14(2), 79-80 (1980) [V.V. Sokolov, A.B. Shabat, (L,A)-Pairs and a Ricatti type substitution, Funct. Anal. Appl., 14(2), 148-150 (1980)].
    91. N.Kh. Ibragimov, A.B. Shabat, O beskonechnykh algebrakh Li–Beklunda, Funkts. analiz i ego pril., 14(4), 79-80 (1980) [N.Kh. Ibragimov, A.B. Shabat, Infinite Lie-Beklund algebras, Funct. Anal. Appl., 14(4), 313-315 (1981)].
    92. A.B. Shabat, Ein inverses Dispersionsproblem. (Russian), Differ. uravn., 15, 1824-1834 (1979).
    93. N.Kh. Ibragimov, A.B. Shabat, The Korteweg–de Vries equation from the point of view of transformation groups (in Russian), Dokl. Akad. nauk SSSR, 244 (1-3), 57-61 (1979) [N.Kh. Ibragimov, A.B. Shabat, The Korteweg–de Vries equation from the point of view of transformation groups, Sov. Phys. Dokl., 24(1), 15-17 (1979)].
    94. A.V. Zhiber, A.B. Shabat, Klein–Gordon equations with a nontrivial group (in Russian), Dokl. Akad. nauk SSSR, 247 (4-6), 1103-1107 (1979) [A.V. Zhiber, A.B. Shabat, Klein–Gordon equations with a nontrivial group, Sov. Phys. Dokl., 24(8), 607-609 (1979)].
    95. A.V. Zhiber, N.Kh. Ibragimov, A.B. Shabat, Equations of Liouville type (in Russian), Dokl. Akad. nauk SSSR, 249, 26-29 (1979) [A.V. Zhiber, N.Kh. Ibragimov, A.B. Shabat, Equations of Liouville type, Sov. Math. Dokl. 20, 1183-1187 (1979)].
    96. V.E. Zakharov, A.B. Shabat, Integrirovanie nelineinykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi rasseyaniya. II, Funkts. analiz i ego pril., 13(3), 13-22 (1979) [V.E. Zakharov, A.B. Shabat, Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II., Funct. Anal. Appl., 13(3), 166-174 (1979)].
    97. A.B. Shabat, Nonlinear evolution equations and the Riemann problem. (Russian), In: Partial differential equations, Proc. All-Union Conf., Moscow 1976, dedic. I. G. Petrovskij, 242-245 (1978).
    98. A.B. Shabat, One-dimensional perturbations of a differential operator, and the inverse scattering problem. (Russian), V sb: Zadachi mekhaniki i matematicheskoi fiziki. Posv. pamyati I.G. Petrovskogo. Pod red. S.L. Soboleva i A.I. Suslova. M.: Nauka, 279-296 (1976).
    99. A.B. Shabat, Obratnaya zadacha rasseyaniya dlya sistemy differentsial’nykh uravnenii, Funkts. analiz i ego pril., 9(3), 75-78 (1975) [A.B. Shabat, Inverse-scattering problem for a system of differential equations, Funct. Anal. Appl., 9(3), 244-247 (1975)].
    100. V.E. Zakharov, A.B. Shabat, Skhema integrirovaniya nelineinykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi rasseyaniya. I, Funkts. analiz i ego pril., 8(3), 43-53 (1974) [V.E. Zakharov, A.B. Shabat, A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I, Funct. Anal. Appl., 8(3), 226-235 (1974)], Scopus: 2-s2.0-0009372301.
    101. A.B. Shabat, Ob uravnenii Kortvega-de Friza, Dokl. Akad. nauk SSSR, 211(6), 1310-1313 (1973) [A.B. Shabat, The Korteweg-de Vries equation, Sov. Math. Dokl. 14, 1266-1270 (1973)].
    102. V.E. Zakharov, A.B. Shabat, O vzaimodeistvii solitonov v ustoichivoi srede, ZhETF, 64 (5), 1627-1639 (1973) [V.E. Zakharov, A.B. Shabat, Interaction between solitons in a stable medium, Sov. Phys. JETP, 37(5), 823-828 (1973)].
    103. A.B. Shabat, One-dimensional scattering theory. I. (Russian), Differ. uravn., 8, 164-178 (1972).
    104. A.B. Shabat, A certain class of Wiener-Hopf type equations. (Russian), Dokl. Akad. nauk SSSR, 205, 546-549 (1972) [A.B. Šabat, A certain class of Wiener-Hopf type equations, Soviet Math. Dokl. 13, 987–992 (1972)].
    105. A.B. Shabat, Obobshchennoe preobrazovanie Fur’e i asimptotika resheniya telegrafnogo uravneniya, Differ. uravn., 7, 157-165 (1971).
    106. V.E. Zakharov, A.B. Shabat, Tonkaya teoriya dvumernoi samofokusirovki i odnomernoi avtomodulyatsii voln v nelineinykh sredakh, ZhETF, 61 (1), 118-134 (1971) [V.E. Zakharov, A.B. Shabat, Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media, Sov. Phys. JETP 34(1), 62-69 (1972)].
    107. A.V. Zhiber, A.B. Shabat, O zadache Koshi dlya nelineinogo uravneniya Shredingera, Differ. uravn., 6(1), 137-146 (1970) [A.V. Ziber, A.B. Shabat, The Cauchy problem for a nonlinear Schrödinger equation, Differ. Equations, 6, 109-116 (1972)].
    108. A.B. Shabat, O potentsialakh s nulevym koeffitsientom otrazheniya, Dinamika sploshnoi sredy, 5, 130-145, Inst. gidrodinamiki SO RAN, Novosibirsk, 1970.
    109. A.B. Shabat, O zadache Koshi dlya uravneniya Ginzburga-Landau, Dinamika sploshnoi sredy, 1, 180-194, Inst. gidrodinamiki SO RAN, Novosibirsk, 1969.
    110. A.B. Shabat, Analog teoremy Kartana-Rado dlya resheniya ellipticheskikh uravnenii, Dokl. Akad. nauk SSSR, 166(6), 1304-1307 (1966) [A.B. Shabat, An analog of the Radó-Cartan theorem for solutions of elliptic equations, Sov. Math. Dokl. 7, 296-299 (1966)].
    111. A.B. Shabat, Ustranimost’ mnozhestv urovnya reshenii ellipticheskikh uravnenii, Dokl. Akad. nauk SSSR, 160(5), 1032-1035 (1965) [A.B. Shabat, The removability of level sets for solutions to elliptic equations, Soviet Math. Dokl. 6, 264–267 (1965)].
    112. A.B. Shabat, Some property of solutions of second-order elliptic equations (in Russian), Dokl. Akad. nauk SSSR, 163(2), 303-305 (1965) [A.B. Shabat, A property of solutions of second-order elliptic equations, Sov. Math. Dokl. 6, 926-938 (1965)].
    113. A.B. Shabat, O dvukh zadachakh na skleivanie dlya ideal’noi neszhimaemoi zhidkosti, Dokl. Akad. nauk SSSR, 150(6), 1242-1245 (1963) [A.B. Shabat, Two Problems in Splicing Solutions of Dirichlet's Problem, Sov. Phys. Dokl., 8, 551 (1963)].
    114. Yu.P. Krasovskii, M.A. Lavrent’ev, N.N. Moiseev, A.M. Ter-Krikorov, A.B. Shabat, Matematicheskie voprosy gidrodinamiki zhidkosti so svobodnymi granitsami, Zh. prikl. mekhaniki i tekhn. fiziki, №4, 3-16 (1963).
    115. A.B. Shabat, Ob odnoi skheme ploskogo dvizheniya zhidkosti pri nalichii na dne transhei, Zh. prikl. mekhaniki i tekhn. fiziki, №4, 68-80 (1962).
    116. A.B. Shabat, Kraevye zadachi s malym parametrom dlya obyknovennykh lineinykh differentsial’nykh uravnenii, Uspekhi mat. nauk, 17:1(103), 235–241 (1962).