Russian Academy of Sciences

Landau Institute for Theoretical Physics

Aleksei B. Shabat

Former staff member (till 2020)

Principal researcher

Doctor of science

Professor

Email:

Publications

    1. R.C. Kulaev, A.B. Shabat, On One Class of Solutions of the Darboux System, In: Operator Theory and Differential Equations. Trends in Mathematics, Ed. by A.G. Kusraev, Zh.D. Totieva, p.79-89 (2021). Birkhäuser, ISBN 978-3-030-49762-0, 978-3-030-49763-7(eBook) [Proc. Int. Conf. Order Analysis and Related Problems of Mathematical Modeling, Vladikavkaz, July 15-20, 2019], Scopus: 2-s2.0-85101108343, RINTs: 46753370, MathSciNet: 4221144.
    2. A.E. Artisevich, A.B. Shabat, Tri teoremy o matritsakh Vandermonda, Vladikavk. matem. zhurn. / Vladikavkaz. Mat. Zh., 22(1), 5-12 (2020), Scopus: 2-s2.0-85088167003, RINTs: 42676846, MathSciNet: 4102881, zbMath: 1463.42009.
    3. R.Ch. Kulaev, A.B. Shabat, Sistema Darbu i razdelenie peremennykh v zadache Gursa dlya uravneniya tret’ego poryadka v ℝ3, Izv. vuzov. Matem., №4, 43-53 (2020) [R.C. Kulaev, A.B. Shabat, Darboux System and Separation of Variables in the Goursat Problem for a Third Order Equation in ℝ3, Russian Mathematics, 64(4), 35-43 (2020)], WoS: 000529686700004, Scopus: 2-s2.0-85083958563, RINTs: 42667313, MathSciNet: 4261432, zbMath: 1445.37048.
    4. A.E. Artisevich, B.S. Bychkov, A.B. Shabat, Mnogochleny Chebyshyova, chisla Katalana i trekhdiagonal’nye matritsy, TMF, 204(1), 3-9 (2020) [A.E. Artisevich, B.S. Bychkov, A.B. Shabat, Chebyshev polynomials, Catalan numbers, and tridiagonal matrices, Theoret. Math. Phys., 204(1), 837-842 (2020)], WoS: 000549724400001, Scopus: 2-s2.0-85088162699, ADS: 2020TMP...204..837A, RINTs: 45404751, MathSciNet: 4133463, zbMath: 1446.39001.
    5. A.A. Allakhverdyan, A.B. Shabat, Proizvedeniya sobstvennykh funktsii i vronskiany, Ufimsk. matem. zhurn., 12(2), 3-9 (2020) [A.A. Allakhverdyan, A.B. Shabat, Products of eigenfunctions and Wronskians, Ufa Math. J., 12(2), 3-9 (2020)], WoS: 000607969100001, Scopus: 2-s2.0-85097566719, RINTs: 44713052, MathSciNet: 4130339, zbMath: 1463.35384.
    6. V.E. Adler, A.B. Shabat, O nekotorykh tochnykh resheniyakh tsepochki Vol’terra, TMF, 201(1), 37-53 (2019) [V.E. Adler, A.B. Shabat, Some exact solutions of the Volterra lattice, Theoret. Math. Phys., 201(1), 1442-1456 (2019)]; arXiv:1903.11901, WoS: 000494479000003, Scopus: 2-s2.0-85074632589, ADS: 2019arXiv190311901A, RINTs: 41560012, MathSciNet: 4017631, zbMath: 1440.37071.
    7. R.Ch. Kulaev, A.B. Shabat, Zakony sokhraneniya v zadache o stupen’ke dlya tsepochki Vol’terra, Ufimsk. matem. zhurn., 11(1), 61-67 (2019) [R.Ch. Kulaev, A.B. Shabat, Conservation laws for Volterra chain with initial step-like condition, Ufa Math. J., 11(1), 63–69 (2019)], WoS: 000466964100005, Scopus: 2-s2.0-85066009359, RINTs: 46520264, MathSciNet: 3962603, zbMath: 1463.34045.
    8. R.Ch. Kulaev, A.K. Pogrebkov, A.B. Shabat, Sistema Darbu kak trekhmernyi analog uravneniya Liuvillya, Izvestiya vuzov. Matematika, №12, 60–69 (2018) [R.Ch. Kulaev, A.K. Pogrebkov, A.B. Shabat, Darboux system as a three-dimensional analogue of the Liouville equation, Russian Mathematics, 62(12), 50-58 (2018)], WoS: 000453361600004, Scopus: 2-s2.0-85058475217, RINTs: 36716286, MathSciNet: 3966389, zbMath: 1412.35211.
    9. V.E. Adler, A.B. Shabat, Tsepochka Vol’terra i chisla Katalana, Pis’ma v ZhETF, 108(12), 834-837 (2018) [V.E. Adler, A.B. Shabat, Volterra chain and Catalan numbers, JETP Lett., 108(12), 825-828 (2018)]; arXiv:1810.13198, WoS: 000460007400011, Scopus: 2-s2.0-85058975942, ADS: 2018JETPL.108..825A, RINTs: 36576020, zbMath: arXiv:1810.13198.
    10. A.B. Shabat, V.E. Adler, Matritsy Kartana v teorii tsepochek Tody–Darbu, TMF, 196(1), 22–29 (2018) [A.B. Shabat, V.E. Adler, Cartan matrices in the Toda–Darboux chain theory, Theor. Math. Phys., 196(1), 957-964 (2018)], WoS: 000440809300002, Scopus: 2-s2.0-85051068584, ADS: 2018TMP...196..957S, RINTs: 35276527, MathSciNet: 3833541, zbMath: 1400.37065.
    11. R.Ch. Kulaev, A.K. Pogrebkov, A.B. Shabat, Sistema Darbu: liuvilleva reduktsiya i yavnoe reshenie, Tr. MIAN, 302, 268-286 (2018) [R.Ch. Kulaev, A.K. Pogrebkov, A.B. Shabat, Darboux System: Liouville Reduction and an Explicit Solution, Proc. Steklov Inst. Math., 302, 250-269 (2018)], WoS: 000454896300012, Scopus: 2-s2.0-85059475494, RINTs: 36503444, MathSciNet: 3894648, zbMath: 1439.35401.
    12. A.B. Shabat, O konstruktivnoi teorii rasseyaniya, TMF, 193(1), 15-24 (2017) [A.B. Shabat, Constructive scattering theory, Theor. Math. Phys., 193(1), 1420-1428 (2017)], WoS: 000415198200002, Scopus: 2-s2.0-85034441327, ADS: 2017TMP...193.1420S, RINTs: 30512367, MathSciNet: 3716523, zbMath: 1387.81362.
    13. A.B. Shabat, M.Kh. Efendiev, O prilozheniyakh formuly Faa-di-Bruno, Ufimsk. matem. zhurn., 9(3), 132-137 (2017) [A.B. Shabat, M.Kh. Efendiev, On applications of Faà-di-Bruno formula, Ufa Math. J., 9(3), 131-136 (2017)], WoS: 000411740000013, Scopus: 2-s2.0-85030026985, RINTs: 30022858, MathSciNet: 3707509, zbMath: 1463.37041.
    14. R.Ch. Kulaev, A.B. Shabat, Nekotorye svoistva reshenii Iosta uravneniya Shryodingera s potentsialom-raspredeleniem, Ufimsk. matem. zhurn., 9(4), 60-73 (2017) [R.Ch. Kulaev, A.B. Shabat, Some properties of Jost functions for Schrödinger equation with distribution potential, Ufa Math. J., 9(4), 59-71 (2017)], WoS: 000424521900007, Scopus: 2-s2.0-85038099326, ADS: -, RINTs: 30562593, MathSciNet: 3738909, zbMath: 1463.34358.
    15. 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, ADS: 2016TMP...189.1712S, RINTs: 27485064, MathSciNet: 3589040, zbMath: 1358.81155.
    16. V.V. Sokolov, A.B. Shabat, O ratsional’nykh resheniyakh uravneniya Rikkati, Uspekhi matem. nauk, 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)], WoS: 000391301300006, Scopus: 2-s2.0-84997173251, ADS: 2016RuMaS..71..787S, RINTs: 26604186, MathSciNet: 3588926, zbMath: 1354.34010.
    17. 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)], WoS: 000411735400003, Scopus: 2-s2.0-85013379967, RINTs: 27512564, MathSciNet: 3605909, zbMath: 1463.34357.
    18. R.Ch. Kulaev, A.B. Shabat, Obratnaya zadacha rasseyaniya dlya finitnykh potentsialov v prostranstve mer Borelya, Preprint YuMI VNTs RAN, Vladikavkaz, №2 (2016) - 19 s, RINTs: 27193710.
    19. 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, Scopus: 2-s2.0-84955455937, ADS: 2015JETPL.102..620S, RINTs: 25021517.
    20. 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, Scopus: 2-s2.0-84928252333, ADS: 2015TMP...183..540S, RINTs: 23421737, MathSciNet: 3399636, zbMath: 1317.37086.
    21. 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, ADS: 2015TMP...184.1067S, RINTs: 24073861, MathSciNet: 3399675, zbMath: 1329.81176.
    22. A.B. Shabat, Vvedenie v teoriyu obratnoi zadachi rasseyaniya, V sbornike: Matematicheskii analiz i matematicheskoe modelirovanie. Trudy X regional’noi shkoly-konferentsii molodykh uchenykh "Vladikavkazskaya molodezhnaya matematicheskaya shkola", s. 101-110 (2015), RINTs: 23707411.
    23. A.B. Shabat, Vvedenie v teoriyu obratnoi zadachi rasseyaniya, Matematichesii analiz i matematicheskoi modelirovanie, s. 101-110 (2015) [Trudy X regional’noi shkoly-konferentsii molodykh uchenykh "Vladikavkazskaya molodezhnaya matematicheskaya shkola", Vladikavkaz, 21–27 iyulya 2014], RINTs: 23707411.
    24. M.Sh. Badakhov, O.Yu. Veremeenko, A.B. Shabat, Ob asimptotike obobshchennykh sobstvennykh znachenii operatora Shredingera, Vladikavkaz. matem. zhurn., 16(4), 9-15 (2014), RINTs: 22753254, MathSciNet: 3550806.
    25. 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, ADS: 2014TMP...179..637S, RINTs: 21826684, MathSciNet: 3305753, zbMath: 1329.34041.
    26. 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], RINTs: 22307324.
    27. 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, ADS: 2013TMP...177.1471S, RINTs: 21277078, MathSciNet: 3230759, zbMath: 1302.35026.
    28. 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, ADS: 2012JPhA...45M5207A, RINTs: 20482435, MathSciNet: 2973648, zbMath: 1297.37030.
    29. A.B. Shabat, Simmetricheskie mnogochleny i zakony sokhraneniya / Symmetrical polynomials and conservation laws, Vladikavkaz. matem. zhurn., 14(4), 83-94 (2012) [A.B. Shabat], RINTs: 18319408, MathSciNet: 3057947, zbMath: 1326.37039.
    30. 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, ADS: 2012TMP...171..435G, RINTs: 20732443, MathSciNet: 3168857, zbMath: 1276.13019.
    31. 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, ADS: 2012TMP...172.1187A, RINTs: 20732516, MathSciNet: 3168742, zbMath: 1283.81093.
    32. 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, ADS: 2012TMP...173.1507S, RINTs: 20732544, MathSciNet: 3172193, zbMath: 1282.13048.
    33. 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) [A.V. Zhiber, R.D. Murtazina, I.T. Habibullin, A.B. Shabat, Characteristic Lie rings and integrable models in mathematical physics, Ufa Math. J., 4(3), 17-85 (2012)], RINTs: 18877678, MathSciNet: 3429920, zbMath: 1299.35020.
    34. 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.
    35. A.B. Shabat, Z.S. El’kanova, O kommutiruyushchikh differentsial’nykh operatorakh v dvumerii, Ufimsk. matem. zhurn., 3(2), 91-99 (2011) [A.B. Shabat, Z.S. Elkanova, Commuting differential operators in two-dimension, Ufa Math. J., 3(2), 89-95 (2011)], WoS: -, Scopus: -, ADS: -, RINTs: 16906051, MathSciNet: 3428996, zbMath: 1249.13019.
    36. M.S. Akbasheva, A.B. Shabat, Teorema o kommutirovanii v glavnom, Ufimsk. matem. zhurn., 3(4), 3-7 (2011) [M.S. Akbasheva, A.B. Shabat, Theorem on commutation in the principal part, Ufa Math. J., 3(4), 3-6 (2011)], WoS: -, Scopus: -, RINTs: 17274597, MathSciNet: 3429009, zbMath: 1249.47029.
    37. M.Kh. Chankaev, A.B. Shabat, Matematicheskii analiz v spektral’noi teorii, Ufa: BashkGU, 2011, 60 str..
    38. A. Shabat, E. Kartashova, Computable Integrability, arXiv:1103.2423, ADS: 2011arXiv1103.2423S.
    39. 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)], WoS: 000276724000002, Scopus: 2-s2.0-77952051600, ADS: 2010TMP...162..276S, RINTs: 20732142, MathSciNet: 2682128, zbMath: 1245.13018.
    40. 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)], WoS: 000273561600002, Scopus: 2-s2.0-76649144486, ADS: 2009TMP...161.1590G, RINTs: 20732112, MathSciNet: 2642192, zbMath: 1188.37054.
    41. 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], WoS: 000266821500005, Scopus: 2-s2.0-56349121300, ADS: 2009LNP...767..139S, RINTs: 14880232, MathSciNet: 2867549, zbMath: 1155.35442.
    42. 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)], WoS: 000261657100002, Scopus: 2-s2.0-58149268989, ADS: 2008TMP...157.1514C, RINTs: 20731950, MathSciNet: 2493776, zbMath: 1155.81372.
    43. A.B. Shabat, Lektsii po teorii solitonov, KChGU, Karachaevsk, 2008, 60 str.
    44. 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, WoS: 000250783100003, Scopus: 2-s2.0-35448982352, ADS: 2007TMP...153.1373A, RINTs: 9918146, MathSciNet: 2402234, zbMath: 1138.37044.
    45. 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].
    46. V.E. Adler, A.B. Shabat, On the one class of hyperbolic systems, SIGMA, 2, 093 (2006); nlin/0612060, WoS: 000207065100092, Scopus: 2-s2.0-84889234679, ADS: 2006SIGMA...2..093A, RINTs: 41744897, MathSciNet: 2280321, zbMath: 1138.35360.
    47. 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, WoS: 000242294000003, Scopus: 2-s2.0-33750572867, ADS: 2006TMP...149.1324A, RINTs: 13517880, MathSciNet: 2297109, zbMath: 1177.37063.
    48. A. Shabat, Universal solitonic hierarchy, J. Nonlinear Math. Phys., 12, Suppl.1, 614-624 (2005), WoS: 000226501000049, Scopus: 2-s2.0-24644497000, ADS: 2005JNMP...12S.614S, RINTs: 13495493, MathSciNet: 2118889, zbMath: 1362.35083.
    49. 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, WoS: 000231408800016, Scopus: 2-s2.0-23044500217, ADS: 2005TMP...144.1004M, RINTs: 13499111, MathSciNet: 2194268, zbMath: 1178.37085.
    50. E. Kartashova, A. Shabat, Computable Integrability. Chapter 5: Factorization of LPDOs, math-ph/0509005, ADS: 2005math.ph...9005K.
    51. E. Kartashova, A. Shabat, Computable Integrability. Chapter 2: Riccati equation, math-ph/0509024, ADS: 2005math.ph...9024K.
    52. A. Shabat, E. Kartashova, Computable Integrability. Chapter 1: General notions and ideas, math-ph/0504020, ADS: 2005math.ph...4020S.
    53. 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, WoS: 000223934900002, Scopus: 2-s2.0-22044442966, ADS: 2004TMP...140.1073M, RINTs: 13464010, MathSciNet: 2101702, zbMath: 1178.37067.
    54. 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, Vol. 132. Kluwer Academic Publishers, Dordrecht, 2004. xiv+297 pp. ISBN: 1-4020-1835-5, MathSciNet: 2156755, zbMath: 1050.35003.
    55. 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], WoS: 000221345900010, MathSciNet: 2153341, zbMath: 1061.35099.
    56. 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, WoS: 000182520700006, Scopus: 2-s2.0-0038729558, ADS: 2003JNMP...10..229A, RINTs: 13435292, MathSciNet: 1976383, zbMath: 1055.35092.
    57. R. Hernández Heredero, A. Shabat, V. Sokolov, A new class of linearizable equations, J. Phys. A 36(47), L605-L614 (2003); nlin/0301001, WoS: 000188194800002, Scopus: 2-s2.0-0344287473, ADS: 2003JPhA...36L.605H, RINTs: 13427638, MathSciNet: 2023333, zbMath: 1076.37524.
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    77. 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)], MathSciNet: 1392673.
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    98. A.B. Shabat, R.I. Yamilov, Lattice representations of integrable systems, Phys. Lett. A 130(4-5), 271-275 (1988), MathSciNet: 0949852.
    99. 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)], MathSciNet: 0976824.
    100. A.V. Mikhailov, A.B. Shabat, R.I. Yamilov, O rasshirenii modulya obratimykh preobrazovanii, 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)], WoS: A1987J301900007, MathSciNet: 902684, zbMath: 0674.35072.
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    103. 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)], WoS: A1986D593000004, MathSciNet: 0831417.
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    105. A.B. Shabat, R.I. Yamilov, O polnom spiske integriruemykh sistem uravnenii vida, Preprint doklada prezidiumu BFAN SSSR. Ufa, 1985? 28 c.
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    108. A.B. Shabat, Usloviya integriruemosti nelineinykh uravnenii, Preprint doklada prezidiumu BFAN SSSR. Ufa, 1983 - 11 s..
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    110. A.B. Shabat (red.), Integriruemye sistemy. Sbornik rabot, Ufa: Bashkirskii filial AN SSSR, 1982 - 116 s,, zbMath: 0553.00006.
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    112. A.B. Shabat, R.I. Yamilov, Eksponentsial’nye sistemy tipa I i matritsy Kartana, Preprint doklada prezidiumu BFAN SSSR. Ufa, 1981 - 22 s.
    113. A.N. Leznov, V.G. Smirnov, A.B. Shabat, Gruppa vnutrennikh simmetrii i usloviya integriruemosti dvumernykh dinamicheskikh sistem, Preprint IFVE OTF 81-11b 1981 - 19 s.
    114. 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)], MathSciNet: 565093, zbMath: 0473.35007.
    115. 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)], Scopus: 2-s2.0-1842505422, MathSciNet: 0575223, zbMath: 0471.35018.
    116. 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)], WoS: A1980LX98800017, MathSciNet: 595739, zbMath: 0452.35053.
    117. A.B. Shabat, Obratnaya zadacha rasseyaniya, Differ. uravn., 15(10), 1824-1834 (1979) [A.B. Shabat, An inverse scattering problem, Differential Equations, 15(10), 1299-1307 (1980)], MathSciNet: 553630, zbMath: 0425.34036.
    118. N. Kh. Ibragimov, A. B. Shabat, Uravnenie Kortevega–de Friza s gruppovoi tochki zreniya, Dokl. Akad. nauk SSSR, 244 (1), 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)], ADS: 1979SPhD...24...15I, MathSciNet: 0523055, zbMath: 0138.36002.
    119. A.V. Zhiber, A.B. Shabat, Uravneniya Kleina–Gordona s netrivial’noi gruppoi, Dokl. Akad. nauk SSSR, 247 (5), 1103-1107 (1979) [A.V. Zhiber, A.B. Shabat, Klein–Gordon equations with a nontrivial group, Sov. Phys. Dokl., 24(8), 607-609 (1979)], ADS: 1979SPhD...24..607Z, MathSciNet: 0550472.
    120. A.V. Zhiber, N.Kh. Ibragimov, A.B. Shabat, Uravneniya tipa Liuvillya, Dokl. Akad. nauk SSSR, 249 (1), 26-29 (1979) [A.V. Zhiber, N.Kh. Ibragimov, A.B. Shabat, Equations of Liouville type, Sov. Math. Dokl. 20, 1183-1187 (1979)], ADS: 1979DoSSR.249...26Z, MathSciNet: 0553975, zbMath: 0455.35007.
    121. 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)], WoS: -, Scopus: 2-s2.0-0002439929, InSpire: 152151, MathSciNet: 545363, zbMath: 0448.35090.
    122. 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)., zbMath: 0499.35058.
    123. 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) [A.B. Shabat, One-dimensional perturbations of a differential operator and the inverse scattering problem, Sel. Math. Sov. 4, 19-35 (1985)], MathSciNet: 0457839, zbMath: 0569.34026.
    124. 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 (1976)], MathSciNet: 0397074, zbMath: 0352.34020.
    125. 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, MathSciNet: 0481668, zbMath: 0303.35024.
    126. A.B. Shabat, Ob uravnenii Kortevega-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)], MathSciNet: 0330800, zbMath: 0289.35069.
    127. 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)], ADS: 1973JETP...37..823Z.
    128. V.E. Zakharov, A.B. Shabat, O vzaimodeistvii solitonov v ustoichivoi srede, Preprint IYaF SO AN SSSR IYaF 30-73, 1973. - 24 s..
    129. A.B. Shabat, Odnomernaya teoriya rasseyaniya. I, Differ. uravn., 8(1), 164-178 (1972) [A.B. Shabat, One-dimensional scattering theory. I, Differ. Equations 8(1), 126-137 (1974)], MathSciNet: 296517, zbMath: 0229.35059.
    130. A.B. Shabat, Ob odnom klasse uravnenii tipa Vinera–Khopfa, Dokl. Akad. nauk SSSR, 205(3), 546-549 (1972) [A.B. Shabat, A certain class of Wiener-Hopf type equations, Soviet Math. Dokl. 13, 987–992 (1972)], MathSciNet: 0308844, zbMath: 0264.45006.
    131. A.B. Shabat, Obobshchennoe preobrazovanie Fur’e i asimptotika reshenii telegrafnogo uravneniya, Differ. uravn., 7(1), 157-165 (1971), MathSciNet: 0280947, zbMath: 0217.14402.
    132. V.E. Zakharov, A.B. Shabat, Tochnaya 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)], WoS: A1972L627800012, ADS: 1972JETP...34...62Z, RINTs: 21757405, MathSciNet: 0406174, EDN: SIDBCR.
    133. V.E. Zakharov, A.B. Shabat, Tochnaya teoriya dvumernoi samofokusirovki i odnomernoi avtomodulyatsii voln v nelineinykh sredakh, Preprint IYaF SO AN SSSR, № 7-71 (1971) - 32 s..
    134. A.V. Zhiber, A.B. Shabat, O zadache Koshi dlya nelineinogo uravneniya Shredingera, Differents. uravneniya, 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)], MathSciNet: 255173, zbMath: 0213.12101.
    135. A.B. Shabat, O potentsialakh s nulevym koeffitsientom otrazheniya, Dinamika sploshnoi sredy, 5, 130-145, Inst. gidrodinamiki SO RAN, Novosibirsk, 1970.
    136. A.B. Shabat, O zadache Koshi dlya uravneniya Ginzburga-Landau, Dinamika sploshnoi sredy, 1, 180-194, Inst. gidrodinamiki SO RAN, Novosibirsk, 1969.
    137. A.B. Shabat, Uravneniya s chastnymi proizvodnymi Ch. 2: Kraevye zadachi. Teoriya potentsiala (Kurs lektsii dlya studentov NGU), Novosib. gos. un-t. - Novosibirsk, 1968 - 84 s.
    138. A.B. Shabat, Uravneniya s chastnymi proizvodnymi Ch. 1: Zadacha Koshi (Kurs lektsii dlya studentov NGU), Novosib. gos. un-t. - Novosibirsk, 1967 - 118 s..
    139. L.V. Ovsyannikov, A.B. Shabat, R.M. Garipov, Zadacha o neustanovivshemsya dvizhenii zhidkosti so svobodnoi granitsei, Novosibirsk: Nauka. Sib. otd-nie, 1967 - 107 s. (Sbornik rabot Teoreticheskogo otdeleniya/ In-t gidrodinamiki SO AN SSSR).
    140. A.B. Shabat, Analog teoremy Rado-Kartana dlya reshenii 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)], MathSciNet: 0199546, zbMath: 0148.09002.
    141. A.B. Shabat, Ob ustranimosti 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)], MathSciNet: 0194736, zbMath: 0138.36002.
    142. A.B. Shabat, Ob odnom svoistve reshenii ellipticheskikh uravnenii vtorogo poryadka, 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)], MathSciNet: 0197969, zbMath: 0141.29603.
    143. A.B. Shabat, O dvukh zadachakh na skleivanie, 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)], ADS: 1963SPhD....8..551S, MathSciNet: 0157000, zbMath: 0139.20402.
    144. Yu.P. Krasovskii, M.A. Lavrent’ev, N.N. Moiseev, A.M. Ter-Krikorov, A.B. Shabat, Matematicheskie voprosy gidrodinamiki zhidkosti so svobodnymi granitsami, Prikl. mekhanika i tekhn. fizika, №4, 3-16 (1963), zbMath: 0133.19603.
    145. A.B. Shabat, Ob odnoi skheme ploskogo dvizheniya zhidkosti pri nalichii na dne transhei, Prikl. mekhanika i tekhn. fizika, №4, 68-80 (1962).
    146. A.B. Shabat, Kraevye zadachi s malym parametrom dlya obyknovennykh lineinykh differentsial’nykh uravnenii, Uspekhi mat. nauk, 17:1(103), 235-241 (1962), MathSciNet: 136825, zbMath: 0106.29303.