Edit Profile (opens in new tab) Sakhnovich, Alexander L. Co-Author Distance Author ID: sakhnovich.alexander-l Published as: Sakhnovich, A. L.; Sakhnovich, Alexander; Sakhnovich, Alexander L.; Sakhnovich, A. more...less Further Spellings: Сахнович Александр Львович External Links: MGP · ORCID · Wikidata · Math-Net.Ru · dblp · GND Documents Indexed: 121 Publications since 1973, including 1 Book and 9 Additional arXiv Preprints Co-Authors: 22 Co-Authors with 48 Joint Publications 828 Co-Co-Authors all top 5 Co-Authors 72 single-authored 17 Fritzsche, Bernd 17 Kirstein, Bernd 16 Roitberg, Inna Ya. 12 Kaashoek, Marinus Adriaan 10 Gohberg, Israel 4 Teschl, Gerald 3 Alpay, Daniel Aron 3 Gesztesy, Fritz 3 Kostenko, Aleksey S. 3 Sakhnovych, Lev Aronovych 2 Lerer, Leonid Efimovich 2 Popovych, Roman O. 1 Blake Allan, S. 1 Eckhardt, Jonathan 1 González Hernández, Manuel 1 Mennicken, Reinhard 1 Michor, Johanna 1 Nichols, Roger 1 Seck Tuoh Mora, Juan Carlos 1 Spitkovsky, Ilya Matvey 1 Tretter, Christiane 1 Zubelli, Jorge P. all top 5 Serials 10 Integral Equations and Operator Theory 9 Inverse Problems 6 Mathematische Nachrichten 5 Journal of Differential Equations 5 Journal of Physics A: Mathematical and Theoretical 5 Operators and Matrices 4 Journal of Mathematical Analysis and Applications 4 Journal of Functional Analysis 4 Linear Algebra and its Applications 3 Journal of Physics A: Mathematical and General 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Mathematical Modelling of Natural Phenomena 2 Discrete and Continuous Dynamical Systems 2 ELA. The Electronic Journal of Linear Algebra 2 Journal of Mathematical Physics, Analysis, Geometry 1 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A 1 IEEE Transactions on Information Theory 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Russian Mathematical Surveys 1 Theoretical and Mathematical Physics 1 Ukrainian Mathematical Journal 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Chaos, Solitons and Fractals 1 Duke Mathematical Journal 1 Journal of Approximation Theory 1 Akademiya Nauk Moldavskoĭ SSR. Ordena Trudovogo Krasnogo Znameni Institut Matematiki s Vychislitel’nym Tsentrom. Matematicheskie Issledovaniya 1 Mathematics of the USSR. Izvestiya 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Revista de la Unión Matemática Argentina 1 Transactions of the American Mathematical Society 1 Soviet Mathematics 1 Constructive Approximation 1 Asymptotic Analysis 1 Differential and Integral Equations 1 IMRN. International Mathematics Research Notices 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Mathematics of the USSR, Sbornik 1 U.S.S.R. Computational Mathematics and Mathematical Physics 1 Matematicheskiĭ Sbornik 1 Indagationes Mathematicae. New Series 1 Russian Mathematics 1 Funktsional’nyĭ Analiz 1 Journal of Difference Equations and Applications 1 Matematicheskaya Fizika, Analiz, Geometriya 1 Documenta Mathematica 1 Positivity 1 Advances in Theoretical and Mathematical Physics 1 De Gruyter Studies in Mathematics 1 Journal of Spectral Theory 1 Journal of Integrable Systems all top 5 Fields 61 Ordinary differential equations (34-XX) 54 Operator theory (47-XX) 44 Partial differential equations (35-XX) 40 Dynamical systems and ergodic theory (37-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 12 Difference and functional equations (39-XX) 8 Quantum theory (81-XX) 8 Systems theory; control (93-XX) 4 Functions of a complex variable (30-XX) 4 Integral equations (45-XX) 4 Numerical analysis (65-XX) 3 Functional analysis (46-XX) 3 Optics, electromagnetic theory (78-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 97 Publications have been cited 704 times in 222 Documents Cited by ▼ Year ▼ Weyl-Titchmarsh theory for Schrödinger operators with strongly singular potentials. Zbl 1248.34027 Kostenko, Aleksey; Sakhnovich, Alexander; Teschl, Gerald 40 2012 Inverse problems and nonlinear evolution equations. Solutions, Darboux matrices and Weyl-Titchmarsh functions. Zbl 1283.47003 Sakhnovich, Alexander L.; Sakhnovich, Lev A.; Roitberg, Inna Ya. 38 2013 Inverse eigenvalue problems for perturbed spherical Schrödinger operators. Zbl 1227.34023 Kostenko, Aleksey; Sakhnovich, Alexander; Teschl, Gerald 33 2010 Dirac type and canonical systems: Spectral and Weyl-Titchmarsh matrix functions, direct and inverse problems. Zbl 1009.34079 Sakhnovich, Alexander 31 2002 Dressing procedure for solutions of non-linear equations and the method of operator identities. Zbl 0805.35129 Sakhnovich, A. L. 31 1994 Canonical systems with rational spectral densities: Explicit formulas and applications. Zbl 0917.34066 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 25 1998 Commutation methods for Schrödinger operators with strongly singular potentials. Zbl 1250.34069 Kostenko, Aleksey; Sakhnovich, Alexander; Teschl, Gerald 23 2012 Pseudo-canonical systems with rational Weyl functions: Explicit formulas and applications. Zbl 0917.34074 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 20 1998 Nonlinear Schrödinger equation on a semi-axis and an inverse problem associated with it. Zbl 0711.35132 Sakhnovich, A. L. 17 1990 Generalized Bäcklund-Darboux transformation: Spectral properties and nonlinear equations. Zbl 0998.34007 Sakhnovich, Alexander 16 2001 Exact solutions of nonlinear equations and the method of operator identities. Zbl 0770.35071 Sakhnovich, Alexander 16 1993 Scattering problems for a canonical system with a pseudo-exponential potential. Zbl 1013.34080 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 16 2002 Krein systems and canonical systems on a finite interval: Accelerants with a jump discontinuity at the origin and continuous potentials. Zbl 1206.34025 Alpay, D.; Gohberg, I.; Kaashoek, M. A.; Lerer, L.; Sakhnovich, A. L. 14 2010 Inverse spectral problems for Schrödinger-type operators with distributional matrix-valued potentials. Zbl 1340.34053 Eckhardt, Jonathan; Gesztesy, Fritz; Nichols, Roger; Sakhnovich, Alexander; Teschl, Gerald 12 2015 Direct and inverse spectral problem for a system of differential equations depending rationally on the spectral parameter. Zbl 1020.34024 Mennicken, R.; Sakhnovich, A. L.; Tretter, C. 12 2001 Skew-self-adjoint discrete and continuous Dirac-type systems: inverse problems and Borg–Marchenko theorems. Zbl 1105.47035 Sakhnovich, Alexander 11 2006 Spectral functions of a canonical system of order \(2n\). Zbl 0776.34066 Sakhnovich, A. L. 11 1992 Inverse problem for Dirac systems with locally square-summable potentials and rectangular Weyl functions. Zbl 1329.34040 Sakhnovich, Alexander 11 2015 Weyl theory and explicit solutions of direct and inverse problems for Dirac system with a rectangular matrix potential. Zbl 1281.34030 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya.; Sakhnovich, A. L. 11 2013 Direct and inverse scattering problem for canonical systems with a strictly pseudo-exponential potential. Zbl 0958.34069 Alpay, D.; Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 10 2000 Dirac type system on the axis: explicit formulae for matrix potentials with singularities and soliton-positon interactions. Zbl 1054.34138 Sakhnovich, Alexander 10 2003 Discrete skew self-adjoint canonical system and the isotropic Heisenberg magnet model. Zbl 1140.47311 Kaashoek, M. A.; Sakhnovich, A. L. 10 2005 Skew-self-adjoint Dirac system with a rectangular matrix potential: Weyl theory, direct and inverse problems. Zbl 1268.34051 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya.; Sakhnovich, A. L. 10 2012 Iterated Bäcklund-Darboux transform for canonical systems. Zbl 0886.35145 Sakhnovich, Alexander 9 1997 Toeplitz matrices with an exponential growth of entries and the first Szegő limit theorem. Zbl 0967.47022 Sakhnovich, Alexander 8 2000 The Goursat problem for the sine-Gordon equation and the inverse spectral problem. Zbl 0924.35145 Sakhnovich, A. L. 8 1992 The inverse approach to Dirac-type systems based on the \(A\)-function concept. Zbl 1470.34053 Gesztesy, Fritz; Sakhnovich, Alexander 8 2020 Sturm-Liouville systems with rational Weyl functions: Explicit formulas and applications. Zbl 0897.34025 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 7 1998 Weyl functions of generalized Dirac systems: integral representation, the inverse problem and discrete interpolation. Zbl 1280.34013 Fritzsche, B.; Kirstein, B.; Sakhnovich, A. L. 7 2012 Asymptotic behavior of spectral functions of an S-node. Zbl 0674.47017 Sakhnovich, A. L. 6 1988 Weyl functions, the inverse problem and special solutions for the system auxiliary to the nonlinear optics equation. Zbl 1151.35105 Sakhnovich, Alexander 6 2008 Recovery of the Dirac system from the rectangular Weyl matrix function. Zbl 1242.34027 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya; Sakhnovich, A. L. 6 2012 Krein systems. Zbl 1191.47061 Alpay, D.; Gohberg, I.; Kaashoek, M. A.; Lerer, L.; Sakhnovich, A. 6 2009 Second harmonic generation: Goursat problem on the semi-strip, Weyl functions and explicit solutions. Zbl 1070.35054 Sakhnovich, Alexander 6 2005 Spectral functions of a canonical system of 2n-th order. Zbl 0718.34112 Sakhnovich, A. L. 6 1990 Dynamical canonical systems and their explicit solutions. Zbl 1379.37126 Sakhnovich, Alexander 6 2017 Matrix Kadomtsev-Petviashvili equation: Matrix identities and explicit non-singular solutions. Zbl 1033.35105 Sakhnovich, A. L. 6 2003 Weyl matrix functions and inverse problems for discrete Dirac-type self-adjoint systems: explicit and general solutions. Zbl 1149.39012 Fritzsche, B.; Kirstein, B.; Roitberg, I.; Sakhnovich, A. L. 6 2008 On the GBDT version of the Bäcklund-Darboux transformation and its applications to linear and nonlinear equations and Weyl theory. Zbl 1200.37070 Sakhnovich, A. 6 2010 GBDT and algebro-geometric approaches to explicit solutions and wave functions for nonlocal NLS. Zbl 1422.35151 Michor, J.; Sakhnovich, A. L. 6 2019 Semiseparable integral operators and explicit solution of an inverse problem for a skew-self-adjoint Dirac-type system. Zbl 1198.34019 Fritzsche, B.; Kirstein, B.; Sakhnovich, A. L. 6 2010 On explicit inversion of a subclass of operators with \(D\)-difference kernels and Weyl theory of the corresponding canonical systems. Zbl 1210.47071 Sakhnovich, Alexander L.; Karelin, Alexander A.; Seck-Tuoh-Mora, J.; Perez-Lechuga, G.; Gonzalez-Hernandez, M. 6 2010 On the compatibility condition for linear systems and a factorization formula for wave functions. Zbl 1232.35032 Sakhnovich, Alexander 5 2012 Modification of V. P. Potapov’s scheme in the indefinite case. Zbl 0818.47032 Sakhnovich, A. L. 5 1994 Iterated Bäcklund-Darboux transformation and transfer matrix-function (nonisospectral case). Zbl 1080.37589 Sakhnovich, A. 5 1996 Dynamical and spectral Dirac systems: response function and inverse problems. Zbl 1347.35078 Sakhnovich, A. L. 5 2015 Hamiltonian systems and Sturm-Liouville equations: Darboux transformation and applications. Zbl 1377.37081 Sakhnovich, Alexander 5 2017 Discrete Dirac system: rectangular Weyl functions, direct and inverse problems. Zbl 1307.39003 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya.; Sakhnovich, A. L. 5 2014 New “Verblunsky-type” coefficients of block Toeplitz and Hankel matrices and of corresponding Dirac and canonical systems. Zbl 1403.15019 Sakhnovich, Alexander 5 2019 On a class of extremal problems. Zbl 0626.47020 Sakhnovich, A. L. 4 1987 Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions. Zbl 1138.35086 Sakhnovich, Alexander 4 2008 Canonical systems on the line with rational spectral densities: Explicit formulas. Zbl 0979.34055 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 4 2000 Sine-Gordon theory in a semi-strip. Zbl 1231.35046 Sakhnovich, Alexander 4 2012 Bundle bispectrality for matrix differential equations. Zbl 1091.34048 Sakhnovich, Alexander; Zubelli, Jorge P. 4 2001 On a certain method of inverting Toeplitz matrices. (Über eine Methode der Inversion Toeplitzscher Matrizen.) Zbl 0331.15016 Sakhnovich, A. L. 4 1973 Completion problems and scattering problems for Dirac type differential equations with singularities. Zbl 1162.34365 Fritzsche, Bernd; Kirstein, Bernd; Sakhnovich, Alexander 4 2006 Non-self-adjoint Dirac-type systems and related nonlinear equations: Wave functions, solutions, and explicit formulas. Zbl 1105.47064 Sakhnovich, Alexander 4 2006 Skew-selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations. Zbl 1376.37111 Fritzsche, B.; Kaashoek, M. A.; Kirstein, B.; Sakhnovich, A. L. 4 2016 Dynamics of electrons and explicit solutions of Dirac-Weyl systems. Zbl 1371.82171 Sakhnovich, Alexander 4 2017 Non-Hermitian matrix Schrödinger equation: Bäcklund–Darboux transformation, Weyl functions and \(\mathcal{PT}\) symmetry. Zbl 1039.81014 Sakhnovich, A. L. 4 2003 On a class of extremal problems. Zbl 0638.47014 Sakhnovich, A. L. 3 1988 Taylor coefficients of a pseudo-exponential potential and the reflection coefficient of the corresponding canonical system. Zbl 1090.34069 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 3 2005 Block-Toeplitz matrices and associated properties of a Gaussian model on a half-axis. Zbl 0608.47026 Sakhnovich, A. L.; Spitkovskij, I. M. 3 1985 On the extension of block Toeplitz matrices. Zbl 0458.47023 Sakhnovich, A. L. 3 1980 Inverse problems for self-adjoint Dirac systems: explicit solutions and stability of the procedure. Zbl 1358.15011 Sakhnovich, Alexander 3 2016 Stability of the procedure of explicit recovery of skew-selfadjoint Dirac systems from rational Weyl matrix functions. Zbl 1373.15025 Fritzsche, Bernd; Kirstein, Bernd; Roitberg, Inna; Sakhnovich, Alexander 3 2017 The discrete self-adjoint Dirac systems of general type: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and the stability of solving of the inverse problem. Zbl 1423.39007 Roitberg, Inna; Sakhnovich, Alexander 3 2018 On the classes of explicit solutions of Dirac, dynamical Dirac and Dirac-Weyl systems with non-vanishing at infinity potentials, their properties and applications. Zbl 1476.34178 Sakhnovich, Alexander 3 2021 Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions. Zbl 1411.39004 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya.; Sakhnovich, A. L. 3 2019 Scattering for general-type Dirac systems on the semi-axis: reflection coefficients and Weyl functions. Zbl 1408.34020 Sakhnovich, Alexander 3 2018 Discrete canonical system and non-Abelian Toda lattice: Bäcklund-Darboux transformation, Weyl functions, and explicit solutions. Zbl 1125.39020 Sakhnovich, A. L. 2 2007 Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem. Zbl 1136.37040 Sakhnovich, Alexander 2 2007 Inverse spectral problem related to the \(N\)-wave equation. Zbl 0956.34071 Sakhnovich, Alexander 2 2000 The time-dependent Schrödinger equation of dimension \(k + 1\): explicit and rational solutions via GBDT and multinodes. Zbl 1231.35190 Sakhnovich, A. L. 2 2011 Continuous and discrete dynamical Schrödinger systems: explicit solutions. Zbl 1387.81207 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya; Sakhnovich, A. L. 2 2018 Bound states of a canonical system with a pseudo-exponential potential. Zbl 0993.34072 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 2 2001 On a new class of structured matrices related to the discrete skew-self-adjoint Dirac systems. Zbl 1176.15018 Fritzsche, Bernd; Kirstein, Bernd; Sakhnovich, Alexander L. 2 2008 The Goursat problem for the sine-Gordon equation. Zbl 0708.35082 Sakhnovich, A. L. 2 1989 KdV equation in the quarter-plane: evolution of the Weyl functions and unbounded solutions. Zbl 1251.35137 Sakhnovich, A. 2 2012 Nonlinear Schrödinger equation in a semi-strip: evolution of the Weyl-Titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditions. Zbl 1308.35280 Sakhnovich, Alexander 2 2015 Construction of the solution of the inverse spectral problem for a system depending rationally on the spectral parameter, Borg-Marchenko-type theorem and sine-Gordon equation. Zbl 1221.34044 Sakhnovich, Alexander 2 2011 Pseudo-exponential-type solutions of wave equations depending on several variables. Zbl 1311.35056 Fritzsche, Bernd; Kirstein, Bernd; Roitberg, Inna Ya.; Sakhnovich, Alexander L. 2 2015 Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications. Zbl 1518.37072 Sakhnovich, Alexander 2 2023 On the class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl-Titchmarsh theory. Zbl 1471.34008 Sakhnovich, Alexander 2 2021 Discrete self-adjoint Dirac systems: asymptotic relations, Weyl functions and Toeplitz matrices. Zbl 1486.39024 Sakhnovich, Alexander 2 2022 Sine-Gordon equation in laboratory coordinates and inverse problem on the semi-axis. Zbl 0858.35113 Sakhnovich, A. L. 1 1996 Erratum: Recovery of the Dirac system from the rectangular Weyl matrix function. Zbl 1251.34023 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya; Sakhnovich, A. L. 1 2012 On an upper bound for mixed error-correcting codes. Zbl 1288.94119 Perkins, S.; Sakhnovich, A. L.; Smith, D. H. 1 2006 A problem of \(N\)-waves on a semi-axis. Zbl 0768.35073 Sakhnovich, A. L. 1 1991 Canonical systems and transfer matrix-functions. Zbl 0869.34067 Sakhnovich, Alexander 1 1997 The \(N\)-wave problem on the half-line. Zbl 0779.35106 Sakhnovich, A. L. 1 1991 Initial value problems for integrable systems on a semi-strip. Zbl 1345.35107 Sakhnovich, Alexander L. 1 2016 On the structure of the inverse to Toeplitz-block Toeplitz matrices and of the corresponding polynomial reflection coefficients. Zbl 1464.15044 Sakhnovich, Alexander 1 2019 GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions of the corresponding non-stationary problems. Zbl 1426.39007 Sakhnovich, Alexander L. 1 2018 Operator identities corresponding to inverse problems for Dirac systems. Zbl 1277.47062 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya.; Sakhnovich, A. L. 1 2012 Explicit solutions of matrix and dynamical Schrödinger equations and of KdV equation in terms of square roots of the generalised matrix eigenvalues. Zbl 1507.34002 Sakhnovich, Alexander 1 2022 On accelerants and their analogs, and on the characterization of the rectangular Weyl functions for Dirac systems with locally square-integrable potentials on a semi-axis. Zbl 1403.34025 Sakhnovich, Alexander 1 2018 Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications. Zbl 1518.37072 Sakhnovich, Alexander 2 2023 Discrete self-adjoint Dirac systems: asymptotic relations, Weyl functions and Toeplitz matrices. Zbl 1486.39024 Sakhnovich, Alexander 2 2022 Explicit solutions of matrix and dynamical Schrödinger equations and of KdV equation in terms of square roots of the generalised matrix eigenvalues. Zbl 1507.34002 Sakhnovich, Alexander 1 2022 On the classes of explicit solutions of Dirac, dynamical Dirac and Dirac-Weyl systems with non-vanishing at infinity potentials, their properties and applications. Zbl 1476.34178 Sakhnovich, Alexander 3 2021 On the class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl-Titchmarsh theory. Zbl 1471.34008 Sakhnovich, Alexander 2 2021 The inverse approach to Dirac-type systems based on the \(A\)-function concept. Zbl 1470.34053 Gesztesy, Fritz; Sakhnovich, Alexander 8 2020 GBDT and algebro-geometric approaches to explicit solutions and wave functions for nonlocal NLS. Zbl 1422.35151 Michor, J.; Sakhnovich, A. L. 6 2019 New “Verblunsky-type” coefficients of block Toeplitz and Hankel matrices and of corresponding Dirac and canonical systems. Zbl 1403.15019 Sakhnovich, Alexander 5 2019 Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions. Zbl 1411.39004 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya.; Sakhnovich, A. L. 3 2019 On the structure of the inverse to Toeplitz-block Toeplitz matrices and of the corresponding polynomial reflection coefficients. Zbl 1464.15044 Sakhnovich, Alexander 1 2019 The discrete self-adjoint Dirac systems of general type: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and the stability of solving of the inverse problem. Zbl 1423.39007 Roitberg, Inna; Sakhnovich, Alexander 3 2018 Scattering for general-type Dirac systems on the semi-axis: reflection coefficients and Weyl functions. Zbl 1408.34020 Sakhnovich, Alexander 3 2018 Continuous and discrete dynamical Schrödinger systems: explicit solutions. Zbl 1387.81207 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya; Sakhnovich, A. L. 2 2018 GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions of the corresponding non-stationary problems. Zbl 1426.39007 Sakhnovich, Alexander L. 1 2018 On accelerants and their analogs, and on the characterization of the rectangular Weyl functions for Dirac systems with locally square-integrable potentials on a semi-axis. Zbl 1403.34025 Sakhnovich, Alexander 1 2018 Dynamical canonical systems and their explicit solutions. Zbl 1379.37126 Sakhnovich, Alexander 6 2017 Hamiltonian systems and Sturm-Liouville equations: Darboux transformation and applications. Zbl 1377.37081 Sakhnovich, Alexander 5 2017 Dynamics of electrons and explicit solutions of Dirac-Weyl systems. Zbl 1371.82171 Sakhnovich, Alexander 4 2017 Stability of the procedure of explicit recovery of skew-selfadjoint Dirac systems from rational Weyl matrix functions. Zbl 1373.15025 Fritzsche, Bernd; Kirstein, Bernd; Roitberg, Inna; Sakhnovich, Alexander 3 2017 Skew-selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations. Zbl 1376.37111 Fritzsche, B.; Kaashoek, M. A.; Kirstein, B.; Sakhnovich, A. L. 4 2016 Inverse problems for self-adjoint Dirac systems: explicit solutions and stability of the procedure. Zbl 1358.15011 Sakhnovich, Alexander 3 2016 Initial value problems for integrable systems on a semi-strip. Zbl 1345.35107 Sakhnovich, Alexander L. 1 2016 Inverse spectral problems for Schrödinger-type operators with distributional matrix-valued potentials. Zbl 1340.34053 Eckhardt, Jonathan; Gesztesy, Fritz; Nichols, Roger; Sakhnovich, Alexander; Teschl, Gerald 12 2015 Inverse problem for Dirac systems with locally square-summable potentials and rectangular Weyl functions. Zbl 1329.34040 Sakhnovich, Alexander 11 2015 Dynamical and spectral Dirac systems: response function and inverse problems. Zbl 1347.35078 Sakhnovich, A. L. 5 2015 Nonlinear Schrödinger equation in a semi-strip: evolution of the Weyl-Titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditions. Zbl 1308.35280 Sakhnovich, Alexander 2 2015 Pseudo-exponential-type solutions of wave equations depending on several variables. Zbl 1311.35056 Fritzsche, Bernd; Kirstein, Bernd; Roitberg, Inna Ya.; Sakhnovich, Alexander L. 2 2015 Discrete Dirac system: rectangular Weyl functions, direct and inverse problems. Zbl 1307.39003 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya.; Sakhnovich, A. L. 5 2014 Inverse problems and nonlinear evolution equations. Solutions, Darboux matrices and Weyl-Titchmarsh functions. Zbl 1283.47003 Sakhnovich, Alexander L.; Sakhnovich, Lev A.; Roitberg, Inna Ya. 38 2013 Weyl theory and explicit solutions of direct and inverse problems for Dirac system with a rectangular matrix potential. Zbl 1281.34030 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya.; Sakhnovich, A. L. 11 2013 Weyl-Titchmarsh theory for Schrödinger operators with strongly singular potentials. Zbl 1248.34027 Kostenko, Aleksey; Sakhnovich, Alexander; Teschl, Gerald 40 2012 Commutation methods for Schrödinger operators with strongly singular potentials. Zbl 1250.34069 Kostenko, Aleksey; Sakhnovich, Alexander; Teschl, Gerald 23 2012 Skew-self-adjoint Dirac system with a rectangular matrix potential: Weyl theory, direct and inverse problems. Zbl 1268.34051 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya.; Sakhnovich, A. L. 10 2012 Weyl functions of generalized Dirac systems: integral representation, the inverse problem and discrete interpolation. Zbl 1280.34013 Fritzsche, B.; Kirstein, B.; Sakhnovich, A. L. 7 2012 Recovery of the Dirac system from the rectangular Weyl matrix function. Zbl 1242.34027 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya; Sakhnovich, A. L. 6 2012 On the compatibility condition for linear systems and a factorization formula for wave functions. Zbl 1232.35032 Sakhnovich, Alexander 5 2012 Sine-Gordon theory in a semi-strip. Zbl 1231.35046 Sakhnovich, Alexander 4 2012 KdV equation in the quarter-plane: evolution of the Weyl functions and unbounded solutions. Zbl 1251.35137 Sakhnovich, A. 2 2012 Erratum: Recovery of the Dirac system from the rectangular Weyl matrix function. Zbl 1251.34023 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya; Sakhnovich, A. L. 1 2012 Operator identities corresponding to inverse problems for Dirac systems. Zbl 1277.47062 Fritzsche, B.; Kirstein, B.; Roitberg, I. Ya.; Sakhnovich, A. L. 1 2012 The time-dependent Schrödinger equation of dimension \(k + 1\): explicit and rational solutions via GBDT and multinodes. Zbl 1231.35190 Sakhnovich, A. L. 2 2011 Construction of the solution of the inverse spectral problem for a system depending rationally on the spectral parameter, Borg-Marchenko-type theorem and sine-Gordon equation. Zbl 1221.34044 Sakhnovich, Alexander 2 2011 Inverse eigenvalue problems for perturbed spherical Schrödinger operators. Zbl 1227.34023 Kostenko, Aleksey; Sakhnovich, Alexander; Teschl, Gerald 33 2010 Krein systems and canonical systems on a finite interval: Accelerants with a jump discontinuity at the origin and continuous potentials. Zbl 1206.34025 Alpay, D.; Gohberg, I.; Kaashoek, M. A.; Lerer, L.; Sakhnovich, A. L. 14 2010 On the GBDT version of the Bäcklund-Darboux transformation and its applications to linear and nonlinear equations and Weyl theory. Zbl 1200.37070 Sakhnovich, A. 6 2010 Semiseparable integral operators and explicit solution of an inverse problem for a skew-self-adjoint Dirac-type system. Zbl 1198.34019 Fritzsche, B.; Kirstein, B.; Sakhnovich, A. L. 6 2010 On explicit inversion of a subclass of operators with \(D\)-difference kernels and Weyl theory of the corresponding canonical systems. Zbl 1210.47071 Sakhnovich, Alexander L.; Karelin, Alexander A.; Seck-Tuoh-Mora, J.; Perez-Lechuga, G.; Gonzalez-Hernandez, M. 6 2010 Krein systems. Zbl 1191.47061 Alpay, D.; Gohberg, I.; Kaashoek, M. A.; Lerer, L.; Sakhnovich, A. 6 2009 Weyl functions, the inverse problem and special solutions for the system auxiliary to the nonlinear optics equation. Zbl 1151.35105 Sakhnovich, Alexander 6 2008 Weyl matrix functions and inverse problems for discrete Dirac-type self-adjoint systems: explicit and general solutions. Zbl 1149.39012 Fritzsche, B.; Kirstein, B.; Roitberg, I.; Sakhnovich, A. L. 6 2008 Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions. Zbl 1138.35086 Sakhnovich, Alexander 4 2008 On a new class of structured matrices related to the discrete skew-self-adjoint Dirac systems. Zbl 1176.15018 Fritzsche, Bernd; Kirstein, Bernd; Sakhnovich, Alexander L. 2 2008 Discrete canonical system and non-Abelian Toda lattice: Bäcklund-Darboux transformation, Weyl functions, and explicit solutions. Zbl 1125.39020 Sakhnovich, A. L. 2 2007 Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem. Zbl 1136.37040 Sakhnovich, Alexander 2 2007 Skew-self-adjoint discrete and continuous Dirac-type systems: inverse problems and Borg–Marchenko theorems. Zbl 1105.47035 Sakhnovich, Alexander 11 2006 Completion problems and scattering problems for Dirac type differential equations with singularities. Zbl 1162.34365 Fritzsche, Bernd; Kirstein, Bernd; Sakhnovich, Alexander 4 2006 Non-self-adjoint Dirac-type systems and related nonlinear equations: Wave functions, solutions, and explicit formulas. Zbl 1105.47064 Sakhnovich, Alexander 4 2006 On an upper bound for mixed error-correcting codes. Zbl 1288.94119 Perkins, S.; Sakhnovich, A. L.; Smith, D. H. 1 2006 Discrete skew self-adjoint canonical system and the isotropic Heisenberg magnet model. Zbl 1140.47311 Kaashoek, M. A.; Sakhnovich, A. L. 10 2005 Second harmonic generation: Goursat problem on the semi-strip, Weyl functions and explicit solutions. Zbl 1070.35054 Sakhnovich, Alexander 6 2005 Taylor coefficients of a pseudo-exponential potential and the reflection coefficient of the corresponding canonical system. Zbl 1090.34069 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 3 2005 Dirac type system on the axis: explicit formulae for matrix potentials with singularities and soliton-positon interactions. Zbl 1054.34138 Sakhnovich, Alexander 10 2003 Matrix Kadomtsev-Petviashvili equation: Matrix identities and explicit non-singular solutions. Zbl 1033.35105 Sakhnovich, A. L. 6 2003 Non-Hermitian matrix Schrödinger equation: Bäcklund–Darboux transformation, Weyl functions and \(\mathcal{PT}\) symmetry. Zbl 1039.81014 Sakhnovich, A. L. 4 2003 Dirac type and canonical systems: Spectral and Weyl-Titchmarsh matrix functions, direct and inverse problems. Zbl 1009.34079 Sakhnovich, Alexander 31 2002 Scattering problems for a canonical system with a pseudo-exponential potential. Zbl 1013.34080 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 16 2002 Generalized Bäcklund-Darboux transformation: Spectral properties and nonlinear equations. Zbl 0998.34007 Sakhnovich, Alexander 16 2001 Direct and inverse spectral problem for a system of differential equations depending rationally on the spectral parameter. Zbl 1020.34024 Mennicken, R.; Sakhnovich, A. L.; Tretter, C. 12 2001 Bundle bispectrality for matrix differential equations. Zbl 1091.34048 Sakhnovich, Alexander; Zubelli, Jorge P. 4 2001 Bound states of a canonical system with a pseudo-exponential potential. Zbl 0993.34072 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 2 2001 Direct and inverse scattering problem for canonical systems with a strictly pseudo-exponential potential. Zbl 0958.34069 Alpay, D.; Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 10 2000 Toeplitz matrices with an exponential growth of entries and the first Szegő limit theorem. Zbl 0967.47022 Sakhnovich, Alexander 8 2000 Canonical systems on the line with rational spectral densities: Explicit formulas. Zbl 0979.34055 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 4 2000 Inverse spectral problem related to the \(N\)-wave equation. Zbl 0956.34071 Sakhnovich, Alexander 2 2000 Canonical systems with rational spectral densities: Explicit formulas and applications. Zbl 0917.34066 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 25 1998 Pseudo-canonical systems with rational Weyl functions: Explicit formulas and applications. Zbl 0917.34074 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 20 1998 Sturm-Liouville systems with rational Weyl functions: Explicit formulas and applications. Zbl 0897.34025 Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L. 7 1998 Iterated Bäcklund-Darboux transform for canonical systems. Zbl 0886.35145 Sakhnovich, Alexander 9 1997 Canonical systems and transfer matrix-functions. Zbl 0869.34067 Sakhnovich, Alexander 1 1997 Iterated Bäcklund-Darboux transformation and transfer matrix-function (nonisospectral case). Zbl 1080.37589 Sakhnovich, A. 5 1996 Sine-Gordon equation in laboratory coordinates and inverse problem on the semi-axis. Zbl 0858.35113 Sakhnovich, A. L. 1 1996 Dressing procedure for solutions of non-linear equations and the method of operator identities. Zbl 0805.35129 Sakhnovich, A. L. 31 1994 Modification of V. P. Potapov’s scheme in the indefinite case. Zbl 0818.47032 Sakhnovich, A. L. 5 1994 Exact solutions of nonlinear equations and the method of operator identities. Zbl 0770.35071 Sakhnovich, Alexander 16 1993 Spectral functions of a canonical system of order \(2n\). Zbl 0776.34066 Sakhnovich, A. L. 11 1992 The Goursat problem for the sine-Gordon equation and the inverse spectral problem. Zbl 0924.35145 Sakhnovich, A. L. 8 1992 A problem of \(N\)-waves on a semi-axis. Zbl 0768.35073 Sakhnovich, A. L. 1 1991 The \(N\)-wave problem on the half-line. Zbl 0779.35106 Sakhnovich, A. L. 1 1991 Nonlinear Schrödinger equation on a semi-axis and an inverse problem associated with it. Zbl 0711.35132 Sakhnovich, A. L. 17 1990 Spectral functions of a canonical system of 2n-th order. Zbl 0718.34112 Sakhnovich, A. L. 6 1990 The Goursat problem for the sine-Gordon equation. Zbl 0708.35082 Sakhnovich, A. L. 2 1989 Asymptotic behavior of spectral functions of an S-node. Zbl 0674.47017 Sakhnovich, A. L. 6 1988 On a class of extremal problems. Zbl 0638.47014 Sakhnovich, A. L. 3 1988 On a class of extremal problems. Zbl 0626.47020 Sakhnovich, A. L. 4 1987 Block-Toeplitz matrices and associated properties of a Gaussian model on a half-axis. Zbl 0608.47026 Sakhnovich, A. L.; Spitkovskij, I. M. 3 1985 On the extension of block Toeplitz matrices. Zbl 0458.47023 Sakhnovich, A. L. 3 1980 On a certain method of inverting Toeplitz matrices. (Über eine Methode der Inversion Toeplitzscher Matrizen.) Zbl 0331.15016 Sakhnovich, A. L. 4 1973 all cited Publications top 5 cited Publications all top 5 Cited by 220 Authors 54 Sakhnovich, Alexander L. 13 Teschl, Gerald 10 Fritzsche, Bernd 10 Gohberg, Israel 10 Kirstein, Bernd 9 Kaashoek, Marinus Adriaan 8 Kostenko, Aleksey S. 7 Eckhardt, Jonathan 7 Roitberg, Inna Ya. 7 Toloza, Julio H. 6 Alpay, Daniel Aron 6 Gesztesy, Fritz 6 Ismailov, Mansur I. 5 Arov, Damir Zyamovich 5 Bondarenko, Natalia P. 5 Dym, Harry 5 Hassan, Mahmood-Ul 5 Mogilevskii, Vadim 5 Silva, Luis O. 4 Daudé, Thierry 4 Hryniv, Rostyslav O. 4 Kamran, Niky 4 Mykytyuk, Yaroslav V. 4 Nicoleau, François 4 Sakhnovych, Lev Aronovych 4 Xu, Xinjian 4 Yang, Chuanfu 3 Liu, Yu 3 Luger, Annemarie 3 Müller-Hoissen, Folkert 3 Popovych, Roman O. 3 Rybalko, Yan 3 Rybkin, Alexei 3 Saleem, Umair 3 Shepelsky, Dmitry 3 Shi, Guoliang 3 Smirnov, Alexander G. 3 Yan, Jun 3 Zubelli, Jorge P. 2 Akçay, Özge 2 Akhtyamov, Azamat Moukhtarovich 2 Albeverio, Sergio A. 2 An, Licong 2 Behrndt, Jussi 2 Bolotnikov, Vladimir 2 Chvartatskyi, Oleksandr 2 Cieśliński, Jan L. 2 Clark, Steve 2 Col, Aynur 2 Gekhtman, Mikhaèl I. 2 Haider, Bushra 2 Kasman, Alex 2 Klaus, Martin 2 Kravchenko, Vladislav V. 2 Makin, Alexander S. 2 Malamud, Mark M. 2 Mamedov, Khanlar R. 2 Mamedov, Khanlar R. 2 Neuner, Christoph 2 Nichols, Roger 2 Puyda, D. V. 2 Rohleder, Jonathan 2 Rovnyak, James 2 Sadovnichiĭ, Viktor Antonovich 2 Schiebold, Cornelia 2 Schmidt, Karl Michael 2 Simon, Barry 2 Sultanaev, Yaudat Talgatovich 2 Torba, Sergii M. 2 Uribe, Alfredo 2 Winkler, Henrik 2 Woracek, Harald 2 Xu, Tao 2 Zhang, Tianli 1 Acharya, Keshav Raj 1 Agler, Jim 1 Aktosun, Tuncay 1 Alonso, Ana Isabel 1 Alshammari, Bader 1 Anan’eva, Aleksandra Yur’evna 1 Andrianov, Alexander A. 1 Basor, Estelle L. 1 Behncke, Horst 1 Beigl, Alexander 1 Bergvelt, Maarten J. 1 Bian, Dongfen 1 Bieganowski, Bartosz 1 Boutet de Monvel, Anne Marie 1 Brown, B. Malcolm 1 Brown, Malcolm W. 1 Brunnhuber, Rainer 1 Budyika, Viktoriya S. 1 Cangzhi, Jia 1 Carillo, Sandra 1 Castillo Pérez, Raúl 1 Chang, Xiangke 1 Chen, Aihua 1 Chen, Gongning 1 Chen, Yang 1 Chitorkin, Egor E. ...and 120 more Authors all top 5 Cited in 85 Serials 19 Journal of Mathematical Analysis and Applications 17 Integral Equations and Operator Theory 12 Journal of Mathematical Physics 12 Journal of Differential Equations 9 Journal of Functional Analysis 8 Mathematische Nachrichten 7 Linear Algebra and its Applications 6 Complex Analysis and Operator Theory 5 Analysis and Mathematical Physics 4 Communications in Mathematical Physics 4 Transactions of the American Mathematical Society 4 Journal of Physics A: Mathematical and Theoretical 4 Journal of Spectral Theory 3 Modern Physics Letters A 3 Inverse Problems 3 Mathematical Methods in the Applied Sciences 3 Theoretical and Mathematical Physics 3 Advances in Mathematics 3 Proceedings of the American Mathematical Society 3 Studies in Applied Mathematics 3 Journal of Mathematical Sciences (New York) 3 Discrete and Continuous Dynamical Systems 3 Communications in Nonlinear Science and Numerical Simulation 3 Annales Henri Poincaré 3 Journal of Nonlinear Mathematical Physics 2 Journal d’Analyse Mathématique 2 Journal of Approximation Theory 2 Monatshefte für Mathematik 2 Mathematical Physics, Analysis and Geometry 2 Journal of Mathematical Physics, Analysis, Geometry 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Operators and Matrices 2 Science China. Mathematics 1 American Mathematical Monthly 1 Applicable Analysis 1 Israel Journal of Mathematics 1 Letters in Mathematical Physics 1 Mathematical Biosciences 1 Mathematical Notes 1 Nonlinearity 1 Physics Letters. A 1 Rocky Mountain Journal of Mathematics 1 Ukrainian Mathematical Journal 1 Wave Motion 1 Chaos, Solitons and Fractals 1 Annales de l’Institut Fourier 1 Applied Mathematics and Computation 1 Bulletin de la Société Mathématique de France 1 Functional Analysis and its Applications 1 Journal of Computational and Applied Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Results in Mathematics 1 Acta Applicandae Mathematicae 1 Physica D 1 Constructive Approximation 1 The Journal of Geometric Analysis 1 L’Enseignement Mathématique. 2e Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 St. Petersburg Mathematical Journal 1 Filomat 1 Journal of Inverse and Ill-Posed Problems 1 The New York Journal of Mathematics 1 Journal of Difference Equations and Applications 1 The Journal of Fourier Analysis and Applications 1 Documenta Mathematica 1 Doklady Mathematics 1 Positivity 1 Annals of Mathematics. Second Series 1 Differential Equations 1 Advances in Difference Equations 1 Boundary Value Problems 1 Journal of Fixed Point Theory and Applications 1 Inverse Problems and Imaging 1 Mathematical Modelling of Natural Phenomena 1 Communications in Theoretical Physics 1 Annals of Functional Analysis 1 Journal of Theoretical Biology 1 Forum of Mathematics, Pi 1 Journal of Function Spaces 1 Advances in Operator Theory all top 5 Cited in 31 Fields 118 Ordinary differential equations (34-XX) 83 Operator theory (47-XX) 66 Partial differential equations (35-XX) 59 Dynamical systems and ergodic theory (37-XX) 35 Quantum theory (81-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 15 Functional analysis (46-XX) 10 Functions of a complex variable (30-XX) 9 Difference and functional equations (39-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Optics, electromagnetic theory (78-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Systems theory; control (93-XX) 4 Integral equations (45-XX) 4 Numerical analysis (65-XX) 3 Approximations and expansions (41-XX) 2 Real functions (26-XX) 2 Mechanics of deformable solids (74-XX) 2 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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