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Sakhnovich, Alexander L.

Author ID: sakhnovich.alexander-l Recent zbMATH articles by "Sakhnovich, Alexander L."
Published as: Sakhnovich, A. L.; Sakhnovich, Alexander; Sakhnovich, Alexander L.; Sakhnovich, A.
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

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

Publications by Year

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 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

Citations by Year

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