Edit Profile (opens in new tab) Shabat, Alekseĭ Borisovich (b. 1937 d. 2020) Co-Author Distance Author ID: shabat.aleksei-borisovich Published as: Shabat, A. B.; Shabat, A.; Shabat, Alekseĭ Borisovich; Shabat, Aleksey Borisovich; Shabat, Alexey B.; Shabat, Alexei more...less Further Spellings: Шабат Алексей Борисович Homepage: https://www.itp.ac.ru/en/persons/shabat-aleksei-borisovich/ External Links: MGP · Wikidata · Math-Net.Ru · IdRef Documents Indexed: 117 Publications since 1962, including 5 Additional arXiv Preprints 3 Contributions as Editor Biographic References: 6 Publications Co-Authors: 63 Co-Authors with 82 Joint Publications 1,438 Co-Co-Authors all top 5 Co-Authors 37 single-authored 14 Adler, Vsevolod Eduardovich 6 Kulaev, Ruslan Chermenovich 6 Martínez Alonso, Luis 6 Sokolov, Vladimir Vyacheslavovich 6 Yamilov, Ravil’ Islamovich 5 Ibragimov, Nail Hairullovich 5 Zhiber, Anatoliĭ Vasil’evich 4 Marikhin, Vladimir G. 4 Mikhajlov, A. V. 3 Gerdt, Vladimir Petrovich 3 Kartashova, Elena A. 3 Leznov, Andreĭ Nikolaevich 3 Mikhailov, Alexander Vasil’evich 3 Svinolupov, S. I. 3 Zharkov, A. Yu. 2 Artisevich, Anzhela Evgen’evna 2 Badakhov, Mukhtar Shamil’evich 2 Degasperis, Antonio 2 Elkanova, Z. S. 2 Khabibullin, Ismagil Talgatovich 2 Pogrebkov, Andrei K. 2 Smirnov, V. G. 2 Veselov, Alexander Petrovich 2 Zakharov, Vladimir Evgen’evich 1 Akbasheva, M. S. 1 Allakhverdyan, Alina Al’bertovna 1 Araf’eva, I. Ya. 1 Boiti, Marco 1 Bychkov, Boris Sergeevich 1 Chankaev, M. Kh. 1 Dobrokhotov, Sergei Yurievich 1 Èfendiev, Magomed Khochalaevich 1 Elhanova, Zariyat Saidakhmatova 1 Fordy, Allan P. 1 Gabiev, R. A. 1 Gershtein, S. S. 1 González-López, Artemio 1 Kholevo, Aleksandr Semënovich 1 Kazakov, Dmitri I. 1 Krasovskij, Yu. P. 1 Kulish, Petr Petrovich 1 Lavrent’ev, Mikhail Alekseevich 1 Levi, Decio 1 Libanov, M. V. 1 Logunov, Anatoliĭ Alekseevich 1 Mañas, Manuel 1 Marshakov, Andrei V. 1 Maslov, Viktor Pavlovich 1 Moiseev, Nikita Nikolaevich 1 Morozov, Alexei Yurievich 1 Murtazina, R. D. 1 Musso, Fabio 1 Pempinelli, Flora 1 Plakida, Nikolay M. 1 Ragnisco, Orlando 1 Rodríguez, Miguel Angel 1 Rubakov, Valery A. 1 Semikhatov, Alexei M. 1 Slavyanov, Sergeĭ Yur’evich 1 Ter-Krikorov, A. M. 1 Tyutin, Igor Viktorovich 1 Urusova, A. B. 1 Veremeenko, Ol’ga Yur’evna all top 5 Serials 36 Theoretical and Mathematical Physics 8 Soviet Mathematics. Doklady 8 Ufimskiĭ Matematicheskiĭ Zhurnal 7 Functional Analysis and its Applications 4 Physics Letters. A 4 Differentsial’nye Uravneniya 4 Differential Equations 3 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 2 Inverse Problems 2 Russian Mathematical Surveys 2 Funktsional’nyĭ Analiz i ego Prilozheniya 2 Soviet Physics. Doklady 2 Russian Mathematics 2 Journal of Nonlinear Mathematical Physics 1 Communications in Mathematical Physics 1 Soviet Scientific Reviews. Section C 1 Teoreticheskaya i Matematicheskaya Fizika 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Selecta Mathematica Sovietica 1 Physica D 1 Leningrad Mathematical Journal 1 Journal of Physics A: Mathematical and General 1 U.S.S.R. Computational Mathematics and Mathematical Physics 1 Canadian Journal of Physics 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Zhurnal Prikladnoĭ Mekhaniki i Tekhnicheskoĭ Fiziki 1 Proceedings of the Steklov Institute of Mathematics 1 NATO Science Series II: Mathematics, Physics and Chemistry 1 Journal of Physics A: Mathematical and Theoretical all top 5 Fields 69 Partial differential equations (35-XX) 49 Dynamical systems and ergodic theory (37-XX) 18 Ordinary differential equations (34-XX) 11 Quantum theory (81-XX) 7 Difference and functional equations (39-XX) 4 Commutative algebra (13-XX) 4 Operator theory (47-XX) 3 General and overarching topics; collections (00-XX) 3 Nonassociative rings and algebras (17-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Computer science (68-XX) 3 Mechanics of particles and systems (70-XX) 2 Integral transforms, operational calculus (44-XX) 2 Numerical analysis (65-XX) 2 Fluid mechanics (76-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 81 Publications have been cited 1,629 times in 1,113 Documents Cited by ▼ Year ▼ A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I. Zbl 0303.35024 Zakharov, V. E.; Shabat, A. B. 336 1974 Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II. Zbl 0448.35090 Zakharov, V. E.; Shabat, A. B. 205 1980 The symmetry approach to classification of integrable equations. Zbl 0741.35070 Mikhailov, A. V.; Shabat, A. B.; Sokolov, V. V. 129 1991 Dressing chains and the spectral theory of the Schrödinger operator. Zbl 0813.35099 Veselov, A. P.; Shabat, A. B. 109 1993 The symmetry approach to the classification of nonlinear equations. Complete lists of integrable systems. Zbl 0646.35010 Mikhajlov, A. V.; Shabat, A. B.; Yamilov, R. I. 83 1987 Symmetry approach to the integrability problem. Zbl 1029.37041 Adler, V. E.; Shabat, A. B.; Yamilov, R. I. 51 2000 The infinite-dimensional dressing dynamical system. Zbl 0762.35098 Shabat, A. 46 1992 Hydrodynamic reductions and solutions of a universal hierarchy. Zbl 1178.37067 Martínez Alonso, Luis; Shabat, A. B. 46 2004 To a transformation theory of two-dimensional integrable systems. Zbl 0962.37509 Shabat, A. B.; Yamilov, R. I. 34 1997 Extension of the module of invertible transformations. Classification of integrable systems. Zbl 0659.35091 Mikhajlov, A. V.; Shabat, A. B.; Yamilov, R. I. 33 1988 Symmetries of nonlinear chains. Zbl 0722.35006 Shabat, A. B.; Yamilov, R. I. 31 1991 Evolutionary equations with nontrivial Lie-Bäcklund group. Zbl 0473.35007 Ibragimov, N. Kh.; Shabat, A. B. 31 1980 The group of internal symmetries and the conditions of integrability of two-dimensional dynamical systems. Zbl 0547.35024 Leznov, A. N.; Smirnov, V. G.; Shabat, A. B. 30 1982 Classification of integrable evolution equations. Zbl 0554.35107 Sokolov, V. V.; Shabat, A. B. 30 1984 Characteristic Lie rings and integrable models in mathematical physics. Zbl 1299.35020 Zhiber, A. V.; Murtazina, R. D.; Habibullin, I. T.; Shabat, A. B. 28 2012 On the prolongation of a hierarchy of hydrodynamic chains. Zbl 1061.35099 Shabat, A. B.; Martínez Alonso, L. 24 2004 Towards a theory of differential constraints of a hydrodynamic hierarchy. Zbl 1055.35092 Martínez Alonso, L.; Shabat, A. B. 20 2003 Inverse-scattering problem for a system of differential equations. Zbl 0352.34020 Shabat, A. B. 19 1976 Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type. Zbl 0996.37072 Martínez Alonso, L.; Shabat, A. B. 19 2002 Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type. Zbl 0997.37045 Martínez Alonso, L.; Shabat, A. B. 17 2002 Model equation of the theory of solitons. Zbl 1138.37044 Adler, V. È.; Shabat, A. B. 16 2007 Infinte Lie-Bäcklund algebras. Zbl 0462.35049 Ibragimov, N. Kh.; Shabat, A. B. 14 1981 Higher symmetries of two-dimensional lattices. Zbl 1020.37585 Shabat, A. B. 13 1995 On the theory of Laplace-Darboux transformations. Zbl 0855.35004 Shabat, A. B. 13 1995 On the Korteweg-de Vries equation. Zbl 0289.35069 Shabat, A. B. 12 1973 The Korteweg-de Vries equation from the point of view of transformation groups. Zbl 0423.35076 Ibragimov, N. Kh.; Shabat, A. B. 11 1979 On a class of Toda chains. Zbl 0978.37502 Adler, V. E.; Shabat, A. B. 11 1997 Generalized Legendre transformations. Zbl 0978.37504 Adler, V. E.; Shabat, A. B. 11 1997 Construction of reflectionless potentials with infinite discrete spectrum. Zbl 0857.34073 Degasperis, A.; Shabat, A. 10 1994 Internal symmetry group and integrability conditions for two-dimensional dynamical systems. Zbl 0504.35023 Leznov, A. N.; Smirnov, V. G.; Shabat, A. B. 10 1982 Toward a theory of integrable hyperbolic equations of third order. Zbl 1297.37030 Adler, V. E.; Shabat, A. B. 10 2012 Lagrangian chains and canonical Bäcklund transformations. Zbl 1029.37042 Adler, V. E.; Marikhin, V. G.; Shabat, A. B. 10 2001 An inverse scattering problem. Zbl 0451.34022 Shabat, A. B. 9 1980 On infinite Lie-Bäcklund algebras. Zbl 0452.35053 Ibragimov, N. Kh.; Shabat, A. B. 9 1980 Equations of Liouville type. Zbl 0455.35007 Zhiber, A. V.; Ibragimov, N. Kh.; Shabat, A. B. 9 1979 Boundary value problem for the KdV equation on a half-line. Zbl 0916.35100 Adler, V. E.; Habibullin, I. T.; Shabat, A. B. 9 1997 Systems of equations \(u_ x=p(u,v)\), \(v_ y=q(u,v)\) having symmetries. Zbl 0599.35023 Zhiber, A. V.; Shabat, A. B. 9 1984 Symmetries – Test of integrability. Zbl 0821.35117 Shabat, A. B.; Mikhailov, A. V. 9 1993 (L,A)-pairs and a Riccati type substitution. Zbl 0494.35025 Sokolov, V. V.; Shabat, A. B. 9 1980 Third version of the dressing method. Zbl 0987.35133 Shabat, A. B. 7 1999 Integrability conditions for systems of two equations of the form \(u_ t=A(u)u_{xx}+F(u,u_ x)\). I. Zbl 0592.35087 Mikhaĭlov, A. V.; Shabat, A. B. 6 1985 Integrability conditions for systems of two equations of the form \(u_ t=A(u)u_{xx}+F(u,u_ x)\). II. Zbl 0606.35042 Mikhajlov, A. V.; Shabat, A. B. 6 1986 Rational interpolation and solitons. Zbl 1329.34041 Shabat, A. B. 5 2014 Symmetric polynomials and conservation laws. Zbl 1326.37039 Shabat, A. B. 5 2012 Integrable lattices. Zbl 0984.37093 Marikhin, V. G.; Shabat, A. B. 5 1999 A new class of linearizable equations. Zbl 1076.37524 Hernández Heredero, R.; Shabat, A.; Sokolov, V. 5 2003 One-dimensional scattering theory. I. Zbl 0229.35059 Shabat, A. B. 4 1972 Conditions for gap series in perturbation theory. Zbl 0569.35065 Leznov, A. N.; Shabat, A. B. 4 1982 Factorization and Poisson correspondences. Zbl 0865.58029 Fordy, A. P.; Shabat, A. B.; Veselov, A. P. 4 1995 Darboux system: Liouville reduction and an explicit solution. Zbl 1439.35401 Kulaev, R. Ch.; Pogrebkov, A. K.; Shabat, A. B. 4 2018 Scattering theory for delta-type potentials. Zbl 1317.37086 Shabat, A. B. 3 2015 Dressing chain for the acoustic spectral problem. Zbl 1177.37063 Adler, V. E.; Shabat, A. B. 3 2006 Universal solitonic hierarchy. Zbl 1362.35083 Shabat, Alexei 3 2005 Some exact solutions of the Volterra lattice. Zbl 1440.37071 Adler, V. E.; Shabat, A. B. 3 2019 Ein inverses Dispersionsproblem. Zbl 0425.34036 Shabat, A. B. 2 1979 Construction of higher local \((2+1)\)-dimensional exponential lattice equations. Zbl 0991.37541 Levi, D.; Ragnisco, O.; Shabat, A. B. 2 1994 Randwertaufgaben mit einem kleinen Parameter für gewöhnliche lineare Differentialgleichungen. Zbl 0106.29303 Shabat, A. B. 2 1962 Darboux system as three-dimensional analog of Liouville equation. Zbl 1412.35211 Kulaev, R. Ch.; Pogrebkov, A. K.; Shabat, A. B. 2 2018 Two problems in splicing solutions of Dirichlet’s problem. Zbl 0139.20402 Shabat, A. B. 2 1963 Symmetries of spectral problems. Zbl 1155.35442 Shabat, A. 2 2009 Universal models of soliton hierarchies. Zbl 1178.37091 Shabat, A. B. 2 2003 On the one class of hyperbolic systems. Zbl 1138.35360 Adler, Vsevolod E.; Shabat, Alexey B. 2 2006 Commuting differential operators. Zbl 1245.13018 Shabat, A. B.; Elkanova, Z. S. 2 2010 On applications of Faà-di-Bruno formula. Zbl 1463.37041 Shabat, Alekseĭ Borisovich; Èfendiev, Magomed Khochalaevich 2 2017 Difference Schrödinger equation and quasisymmetric polynomials. Zbl 1329.81176 Shabat, A. B. 1 2015 First integrals of generalized Toda chains. Zbl 0981.37029 Adler, V. È.; Shabat, A. B. 1 1998 Dressing chains and lattices. Zbl 0965.35163 Shabat, A. 1 2000 Functional Cantor equation. Zbl 1358.81155 Shabat, A. B. 1 2016 On extending the module of invertible transformations. Zbl 0674.35072 Mikhajlov, A. V.; Shabat, A. B.; Yamilov, R. I. 1 1987 Construction of reflectionless potentials with infinitely many discrete eigenvalues. Zbl 0787.35076 Degasperis, A.; Shabat, A. 1 1993 Über das Cauchyproblem für die nichtlineare Schrödingergleichung. Zbl 0213.12101 Zhiber, A. V.; Shabat, A. B. 1 1970 Two-sided Darboux transformations. Zbl 1282.13048 Shabat, A. B.; Élkanova, Z. S.; Urusova, A. B. 1 2012 Differential operators commuting in the principal part. Zbl 1276.13019 Gabiev, R. A.; Shabat, A. B. 1 2012 A nonlinear eigenvalue problem. Zbl 1155.81372 Chankaev, M. Kh.; Shabat, A. B. 1 2008 One-dimensional perturbations of a differential operator and the inverse scattering problem. Zbl 0569.34026 Shabat, A. B. 1 1985 Elementary Darboux transformations and factorization. Zbl 1178.37085 Musso, F.; Shabat, A. B. 1 2005 The structure of polynomial conservation laws. Zbl 1188.37054 Garifullin, R. N.; Shabat, A. B. 1 2009 Computer algebra application for investigating integrability of nonlinear evolution systems. Zbl 1209.68676 Gerdt, V. P.; Shabat, A. B.; Svinolupov, S. I.; Zharkov, A. Yu. 1 1989 Darboux system and separation of variables in the Goursat problem for a third order equation in \(\mathbb{R}^3\). Zbl 1445.37048 Kulaev, R. Ch.; Shabat, A. B. 1 2020 Chebyshev polynomials, Catalan numbers, and tridiagonal matrices. Zbl 1446.39001 Artisevich, A. E.; Bychkov, B. S.; Shabat, A. B. 1 2020 Some properties of Jost functions for Schrödinger equation with distribution potential. Zbl 1463.34358 Kulaev, Ruslan Chermenovich; Shabat, Alekseĭ Borisovich 1 2017 Darboux system and separation of variables in the Goursat problem for a third order equation in \(\mathbb{R}^3\). Zbl 1445.37048 Kulaev, R. Ch.; Shabat, A. B. 1 2020 Chebyshev polynomials, Catalan numbers, and tridiagonal matrices. Zbl 1446.39001 Artisevich, A. E.; Bychkov, B. S.; Shabat, A. B. 1 2020 Some exact solutions of the Volterra lattice. Zbl 1440.37071 Adler, V. E.; Shabat, A. B. 3 2019 Darboux system: Liouville reduction and an explicit solution. Zbl 1439.35401 Kulaev, R. Ch.; Pogrebkov, A. K.; Shabat, A. B. 4 2018 Darboux system as three-dimensional analog of Liouville equation. Zbl 1412.35211 Kulaev, R. Ch.; Pogrebkov, A. K.; Shabat, A. B. 2 2018 On applications of Faà-di-Bruno formula. Zbl 1463.37041 Shabat, Alekseĭ Borisovich; Èfendiev, Magomed Khochalaevich 2 2017 Some properties of Jost functions for Schrödinger equation with distribution potential. Zbl 1463.34358 Kulaev, Ruslan Chermenovich; Shabat, Alekseĭ Borisovich 1 2017 Functional Cantor equation. Zbl 1358.81155 Shabat, A. B. 1 2016 Scattering theory for delta-type potentials. Zbl 1317.37086 Shabat, A. B. 3 2015 Difference Schrödinger equation and quasisymmetric polynomials. Zbl 1329.81176 Shabat, A. B. 1 2015 Rational interpolation and solitons. Zbl 1329.34041 Shabat, A. B. 5 2014 Characteristic Lie rings and integrable models in mathematical physics. Zbl 1299.35020 Zhiber, A. V.; Murtazina, R. D.; Habibullin, I. T.; Shabat, A. B. 28 2012 Toward a theory of integrable hyperbolic equations of third order. Zbl 1297.37030 Adler, V. E.; Shabat, A. B. 10 2012 Symmetric polynomials and conservation laws. Zbl 1326.37039 Shabat, A. B. 5 2012 Two-sided Darboux transformations. Zbl 1282.13048 Shabat, A. B.; Élkanova, Z. S.; Urusova, A. B. 1 2012 Differential operators commuting in the principal part. Zbl 1276.13019 Gabiev, R. A.; Shabat, A. B. 1 2012 Commuting differential operators. Zbl 1245.13018 Shabat, A. B.; Elkanova, Z. S. 2 2010 Symmetries of spectral problems. Zbl 1155.35442 Shabat, A. 2 2009 The structure of polynomial conservation laws. Zbl 1188.37054 Garifullin, R. N.; Shabat, A. B. 1 2009 A nonlinear eigenvalue problem. Zbl 1155.81372 Chankaev, M. Kh.; Shabat, A. B. 1 2008 Model equation of the theory of solitons. Zbl 1138.37044 Adler, V. È.; Shabat, A. B. 16 2007 Dressing chain for the acoustic spectral problem. Zbl 1177.37063 Adler, V. E.; Shabat, A. B. 3 2006 On the one class of hyperbolic systems. Zbl 1138.35360 Adler, Vsevolod E.; Shabat, Alexey B. 2 2006 Universal solitonic hierarchy. Zbl 1362.35083 Shabat, Alexei 3 2005 Elementary Darboux transformations and factorization. Zbl 1178.37085 Musso, F.; Shabat, A. B. 1 2005 Hydrodynamic reductions and solutions of a universal hierarchy. Zbl 1178.37067 Martínez Alonso, Luis; Shabat, A. B. 46 2004 On the prolongation of a hierarchy of hydrodynamic chains. Zbl 1061.35099 Shabat, A. B.; Martínez Alonso, L. 24 2004 Towards a theory of differential constraints of a hydrodynamic hierarchy. Zbl 1055.35092 Martínez Alonso, L.; Shabat, A. B. 20 2003 A new class of linearizable equations. Zbl 1076.37524 Hernández Heredero, R.; Shabat, A.; Sokolov, V. 5 2003 Universal models of soliton hierarchies. Zbl 1178.37091 Shabat, A. B. 2 2003 Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type. Zbl 0996.37072 Martínez Alonso, L.; Shabat, A. B. 19 2002 Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type. Zbl 0997.37045 Martínez Alonso, L.; Shabat, A. B. 17 2002 Lagrangian chains and canonical Bäcklund transformations. Zbl 1029.37042 Adler, V. E.; Marikhin, V. G.; Shabat, A. B. 10 2001 Symmetry approach to the integrability problem. Zbl 1029.37041 Adler, V. E.; Shabat, A. B.; Yamilov, R. I. 51 2000 Dressing chains and lattices. Zbl 0965.35163 Shabat, A. 1 2000 Third version of the dressing method. Zbl 0987.35133 Shabat, A. B. 7 1999 Integrable lattices. Zbl 0984.37093 Marikhin, V. G.; Shabat, A. B. 5 1999 First integrals of generalized Toda chains. Zbl 0981.37029 Adler, V. È.; Shabat, A. B. 1 1998 To a transformation theory of two-dimensional integrable systems. Zbl 0962.37509 Shabat, A. B.; Yamilov, R. I. 34 1997 On a class of Toda chains. Zbl 0978.37502 Adler, V. E.; Shabat, A. B. 11 1997 Generalized Legendre transformations. Zbl 0978.37504 Adler, V. E.; Shabat, A. B. 11 1997 Boundary value problem for the KdV equation on a half-line. Zbl 0916.35100 Adler, V. E.; Habibullin, I. T.; Shabat, A. B. 9 1997 Higher symmetries of two-dimensional lattices. Zbl 1020.37585 Shabat, A. B. 13 1995 On the theory of Laplace-Darboux transformations. Zbl 0855.35004 Shabat, A. B. 13 1995 Factorization and Poisson correspondences. Zbl 0865.58029 Fordy, A. P.; Shabat, A. B.; Veselov, A. P. 4 1995 Construction of reflectionless potentials with infinite discrete spectrum. Zbl 0857.34073 Degasperis, A.; Shabat, A. 10 1994 Construction of higher local \((2+1)\)-dimensional exponential lattice equations. Zbl 0991.37541 Levi, D.; Ragnisco, O.; Shabat, A. B. 2 1994 Dressing chains and the spectral theory of the Schrödinger operator. Zbl 0813.35099 Veselov, A. P.; Shabat, A. B. 109 1993 Symmetries – Test of integrability. Zbl 0821.35117 Shabat, A. B.; Mikhailov, A. V. 9 1993 Construction of reflectionless potentials with infinitely many discrete eigenvalues. Zbl 0787.35076 Degasperis, A.; Shabat, A. 1 1993 The infinite-dimensional dressing dynamical system. Zbl 0762.35098 Shabat, A. 46 1992 The symmetry approach to classification of integrable equations. Zbl 0741.35070 Mikhailov, A. V.; Shabat, A. B.; Sokolov, V. V. 129 1991 Symmetries of nonlinear chains. Zbl 0722.35006 Shabat, A. B.; Yamilov, R. I. 31 1991 Computer algebra application for investigating integrability of nonlinear evolution systems. Zbl 1209.68676 Gerdt, V. P.; Shabat, A. B.; Svinolupov, S. I.; Zharkov, A. Yu. 1 1989 Extension of the module of invertible transformations. Classification of integrable systems. Zbl 0659.35091 Mikhajlov, A. V.; Shabat, A. B.; Yamilov, R. I. 33 1988 The symmetry approach to the classification of nonlinear equations. Complete lists of integrable systems. Zbl 0646.35010 Mikhajlov, A. V.; Shabat, A. B.; Yamilov, R. I. 83 1987 On extending the module of invertible transformations. Zbl 0674.35072 Mikhajlov, A. V.; Shabat, A. B.; Yamilov, R. I. 1 1987 Integrability conditions for systems of two equations of the form \(u_ t=A(u)u_{xx}+F(u,u_ x)\). II. Zbl 0606.35042 Mikhajlov, A. V.; Shabat, A. B. 6 1986 Integrability conditions for systems of two equations of the form \(u_ t=A(u)u_{xx}+F(u,u_ x)\). I. Zbl 0592.35087 Mikhaĭlov, A. V.; Shabat, A. B. 6 1985 One-dimensional perturbations of a differential operator and the inverse scattering problem. Zbl 0569.34026 Shabat, A. B. 1 1985 Classification of integrable evolution equations. Zbl 0554.35107 Sokolov, V. V.; Shabat, A. B. 30 1984 Systems of equations \(u_ x=p(u,v)\), \(v_ y=q(u,v)\) having symmetries. Zbl 0599.35023 Zhiber, A. V.; Shabat, A. B. 9 1984 The group of internal symmetries and the conditions of integrability of two-dimensional dynamical systems. Zbl 0547.35024 Leznov, A. N.; Smirnov, V. G.; Shabat, A. B. 30 1982 Internal symmetry group and integrability conditions for two-dimensional dynamical systems. Zbl 0504.35023 Leznov, A. N.; Smirnov, V. G.; Shabat, A. B. 10 1982 Conditions for gap series in perturbation theory. Zbl 0569.35065 Leznov, A. N.; Shabat, A. B. 4 1982 Infinte Lie-Bäcklund algebras. Zbl 0462.35049 Ibragimov, N. Kh.; Shabat, A. B. 14 1981 Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II. Zbl 0448.35090 Zakharov, V. E.; Shabat, A. B. 205 1980 Evolutionary equations with nontrivial Lie-Bäcklund group. Zbl 0473.35007 Ibragimov, N. Kh.; Shabat, A. B. 31 1980 An inverse scattering problem. Zbl 0451.34022 Shabat, A. B. 9 1980 On infinite Lie-Bäcklund algebras. Zbl 0452.35053 Ibragimov, N. Kh.; Shabat, A. B. 9 1980 (L,A)-pairs and a Riccati type substitution. Zbl 0494.35025 Sokolov, V. V.; Shabat, A. B. 9 1980 The Korteweg-de Vries equation from the point of view of transformation groups. Zbl 0423.35076 Ibragimov, N. Kh.; Shabat, A. B. 11 1979 Equations of Liouville type. Zbl 0455.35007 Zhiber, A. V.; Ibragimov, N. Kh.; Shabat, A. B. 9 1979 Ein inverses Dispersionsproblem. Zbl 0425.34036 Shabat, A. B. 2 1979 Inverse-scattering problem for a system of differential equations. Zbl 0352.34020 Shabat, A. B. 19 1976 A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I. Zbl 0303.35024 Zakharov, V. E.; Shabat, A. B. 336 1974 On the Korteweg-de Vries equation. Zbl 0289.35069 Shabat, A. B. 12 1973 One-dimensional scattering theory. I. Zbl 0229.35059 Shabat, A. B. 4 1972 Über das Cauchyproblem für die nichtlineare Schrödingergleichung. Zbl 0213.12101 Zhiber, A. V.; Shabat, A. B. 1 1970 Two problems in splicing solutions of Dirichlet’s problem. Zbl 0139.20402 Shabat, A. B. 2 1963 Randwertaufgaben mit einem kleinen Parameter für gewöhnliche lineare Differentialgleichungen. Zbl 0106.29303 Shabat, A. B. 2 1962 all cited Publications top 5 cited Publications all top 5 Cited by 1,014 Authors 40 Shabat, Alekseĭ Borisovich 37 Khabibullin, Ismagil Talgatovich 27 Adler, Vsevolod Eduardovich 20 Morozov, Oleg I. 20 Sokolov, Vladimir Vyacheslavovich 17 Fan, Engui 16 Khakimova, Aĭgul’ Rinatovna 16 Mikhailov, Alexander Vasil’evich 13 Ferapontov, Evgeny Vladimirovich 13 Sergyeyev, Artur 13 Wang, Jingping 12 Pogrebkov, Andrei K. 12 Prykarpatsky, Anatoliy Karolevych 12 Tian, Shoufu 11 Ablowitz, Mark Jay 11 Gerdzhikov, Vladimir Stefanov 11 Meshkov, Anatoly G. 11 Prykarpatsky, Yarema Anatoliyovych 11 Zenchuk, Alexandre I. 10 Fokas, Athanassios S. 10 Grinevich, Pëtr Georgievich 10 Konopelchenko, Boris Georgievich 10 Krasil’shchik, Iosif Semënovich 10 Krichever, Igor’ Moiseevich 10 Yamilov, Ravil’ Islamovich 9 Boiti, Marco 9 Euler, Norbert 9 Orlov, Aleksandr Yu. 9 Pempinelli, Flora 9 Santini, Paolo Maria 9 Zheltukhina, Natalya A. 8 Boutet de Monvel, Anne Marie 8 Euler, Marianna 8 Fordy, Allan P. 8 Geng, Xianguo 8 Khusnutdinova, Karima Robertovna 8 Reyes, Enrique G. 8 Vojčák, Petr 8 Zakharov, Vladimir Evgen’evich 7 Abenda, Simonetta 7 Bogdanov, Leonid Vital’evich 7 Hone, Andrew N. W. 7 Kappeler, Thomas 7 Kiselev, Arthemy V. 7 Novikov, Vladimir S. 7 Novokshenov, Viktor Yur’evich 7 Sahadevan, Ramajayam 7 Zhang, Yufeng 7 Zheltukhin, Kostyantyn 6 Baran, Hynek 6 Blackmore, Denis L. 6 Błaszak, Maciej 6 Clarkson, Peter A. 6 He, Jingsong 6 Ivanov, Rossen I. 6 Marikhin, Vladimir G. 6 Marquette, Ian 6 Pavlov, Maxim V. 6 Prinari, Barbara 6 Sakhnovich, Alexander L. 6 Xenitidis, Pavlos 5 Anco, Stephen C. 5 Balakhnev, M. Yu. 5 Demskoi, Dmitry K. 5 Doikou, Anastasia 5 Dubrovsky, V. G. 5 Foursov, Mikhail V. 5 Grahovski, Georgi G. 5 Harnad, John 5 Hentosh, Oksana E. 5 Hereman, Willy A. 5 Khalique, Chaudry Masood 5 Levi, Decio 5 Liu, Yue 5 Millionshchikov, Dmitriĭ Vladimirovich 5 Sanders, Jan A. 5 Segur, Harvey 5 Shepelsky, Dmitry 5 Svinolupov, S. I. 5 Topalov, Peter J. 5 van der Kamp, Peter H. 5 Zharinov, Victor Victorovich 5 Zhu, Junyi 4 Calogero, Francesco A. 4 Chen, Yong 4 Domrin, Andrei Victorovich 4 Dorfmeister, Josef F. 4 Gómez-Ullate, David 4 Guo, Boling 4 Hernández Heredero, Rafael 4 Ibragimov, Nail Hairullovich 4 Ismailov, Mansur I. 4 Kac, Victor 4 Kruglikov, Boris S. 4 Lenells, Jonatan 4 Li, Biao 4 Li, Chuanzhong 4 Li, Zhiqiang 4 Luo, Jinghua 4 Ma, Wen-Xiu ...and 914 more Authors all top 5 Cited in 190 Serials 156 Journal of Mathematical Physics 150 Theoretical and Mathematical Physics 49 Journal of Nonlinear Mathematical Physics 44 Journal of Physics A: Mathematical and Theoretical 38 Journal of Geometry and Physics 35 Physica D 34 Communications in Mathematical Physics 27 Journal of Mathematical Analysis and Applications 24 Functional Analysis and its Applications 21 Ufimskiĭ Matematicheskiĭ Zhurnal 18 Studies in Applied Mathematics 16 Physics Letters. A 15 Letters in Mathematical Physics 15 Journal of Mathematical Sciences (New York) 14 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 13 Chaos, Solitons and Fractals 13 Journal of Differential Equations 11 Journal of Soviet Mathematics 11 Acta Applicandae Mathematicae 10 Applied Mathematics and Computation 9 Mathematical Notes 9 Nonlinearity 9 Applied Mathematics Letters 9 Communications in Nonlinear Science and Numerical Simulation 7 Nuclear Physics. B 7 Ukrainian Mathematical Journal 7 Advances in Mathematics 7 Duke Mathematical Journal 7 Publications of the Research Institute for Mathematical Sciences, Kyoto University 7 Nonlinear Dynamics 6 Applicable Analysis 6 Reports on Mathematical Physics 6 Lobachevskii Journal of Mathematics 5 Journal of Fluid Mechanics 5 Wave Motion 5 Journal of Functional Analysis 5 Differential Geometry and its Applications 5 Nonlinear Analysis. Real World Applications 5 Advances in Mathematical Physics 5 Symmetry 5 Analysis and Mathematical Physics 4 Journal of Applied Mathematics and Mechanics 4 Journal of Computational and Applied Mathematics 4 Mathematics and Computers in Simulation 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Journal of Symbolic Computation 4 International Journal of Mathematics 4 Journal of Nonlinear Science 4 Mathematical Physics, Analysis and Geometry 4 Regular and Chaotic Dynamics 4 International Journal of Geometric Methods in Modern Physics 4 Advances in Difference Equations 3 International Journal of Modern Physics A 3 Classical and Quantum Gravity 3 Computer Physics Communications 3 Russian Mathematical Surveys 3 Reviews in Mathematical Physics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Mathematische Nachrichten 3 Mathematische Zeitschrift 3 Siberian Mathematical Journal 3 SIAM Journal on Mathematical Analysis 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Bulletin des Sciences Mathématiques 3 Journal of High Energy Physics 3 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 3 Waves in Random and Complex Media 3 Proceedings of the Steklov Institute of Mathematics 3 Communications in Theoretical Physics 3 Japanese Journal of Mathematics. 3rd Series 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Computers & Mathematics with Applications 2 Communications on Pure and Applied Mathematics 2 Bulletin of the London Mathematical Society 2 Integral Equations and Operator Theory 2 Mathematische Annalen 2 Proceedings of the American Mathematical Society 2 Quarterly of Applied Mathematics 2 Transactions of the Moscow Mathematical Society 2 Ergodic Theory and Dynamical Systems 2 Applied Numerical Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 European Journal of Applied Mathematics 2 Journal of Dynamics and Differential Equations 2 St. Petersburg Mathematical Journal 2 Turkish Journal of Mathematics 2 Fractals 2 Selecta Mathematica. New Series 2 Abstract and Applied Analysis 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Foundations of Computational Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Frontiers of Mathematics in China 2 Journal of Geometric Mechanics 2 Journal of Siberian Federal University. Mathematics & Physics 1 Modern Physics Letters B 1 International Journal of Modern Physics B 1 Computers and Fluids 1 International Journal of Theoretical Physics 1 Inverse Problems ...and 90 more Serials all top 5 Cited in 49 Fields 719 Partial differential equations (35-XX) 640 Dynamical systems and ergodic theory (37-XX) 128 Quantum theory (81-XX) 124 Ordinary differential equations (34-XX) 95 Global analysis, analysis on manifolds (58-XX) 89 Difference and functional equations (39-XX) 74 Nonassociative rings and algebras (17-XX) 55 Differential geometry (53-XX) 50 Fluid mechanics (76-XX) 42 Mechanics of particles and systems (70-XX) 36 Algebraic geometry (14-XX) 29 Special functions (33-XX) 29 Operator theory (47-XX) 24 Numerical analysis (65-XX) 21 Topological groups, Lie groups (22-XX) 16 Functions of a complex variable (30-XX) 16 Optics, electromagnetic theory (78-XX) 16 Statistical mechanics, structure of matter (82-XX) 13 Relativity and gravitational theory (83-XX) 12 Computer science (68-XX) 10 Approximations and expansions (41-XX) 7 Commutative algebra (13-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Integral equations (45-XX) 6 Functional analysis (46-XX) 6 Mechanics of deformable solids (74-XX) 5 Combinatorics (05-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Real functions (26-XX) 4 Integral transforms, operational calculus (44-XX) 4 Probability theory and stochastic processes (60-XX) 3 General and overarching topics; collections (00-XX) 3 Number theory (11-XX) 3 Associative rings and algebras (16-XX) 3 Group theory and generalizations (20-XX) 3 Algebraic topology (55-XX) 2 History and biography (01-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geometry (51-XX) 2 Manifolds and cell complexes (57-XX) 2 Geophysics (86-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 \(K\)-theory (19-XX) 1 Potential theory (31-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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