# zbMATH — the first resource for mathematics

## Brezhnev, Yurii V.

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 Author ID: brezhnev.yurii-v Published as: Brezhnev, Yu. V.; Brezhnev, Yurii V.; Brežnev, Yu. V.
 Documents Indexed: 25 Publications since 1995
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#### Co-Authors

 20 single-authored 1 Andreev, Vladimir A. 1 Lyakhovich, Simon L. 1 Sharapov, Alexey A. 1 Sherratt, Jonathan A. 1 Tsvetkova, Anna V. 1 Ustinov, Nikolai V.
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#### Serials

 3 Journal of Mathematical Physics 3 Theoretical and Mathematical Physics 2 Physics Letters. A 2 Russian Mathematical Surveys 2 Journal of Differential Equations 1 Mathematical Notes 1 Reports on Mathematical Physics 1 Journal of Geometry and Physics 1 Physica D 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 St. Petersburg Mathematical Journal 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Moscow Mathematical Journal 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
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#### Fields

 12 Ordinary differential equations (34-XX) 11 Dynamical systems and ergodic theory (37-XX) 10 Special functions (33-XX) 7 Partial differential equations (35-XX) 5 Functions of a complex variable (30-XX) 4 Algebraic geometry (14-XX) 3 Number theory (11-XX) 3 Quantum theory (81-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Fluid mechanics (76-XX)

#### Citations contained in zbMATH

18 Publications have been cited 72 times in 54 Documents Cited by Year
Finite-gap potentials with trigonal curves. Zbl 1087.34561
Brezhnev, Yu. V.
2002
Darboux transformation and some multi-phase solutions of the Dodd-Bullough-Tzitzeica equation: $$U_{xt}=e^ U-e^{-2U}$$. Zbl 1072.35555
Brezhnev, Yurii V.
1996
Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials. Zbl 1248.81032
Brezhnev, Yurii V.
2012
A $$\tau$$-function solution of the sixth Painlevé transcendent. Zbl 1185.37137
Brezhnev, Yu. V.
2009
Non-canonical extension of $$\theta$$-functions and modular integrability of $$\vartheta$$-constants. Zbl 1318.33034
Brezhnev, Yurii V.
2013
What does integrability of finite-gap or soliton potentials mean? Zbl 1153.37411
Brezhnev, Yurii V.
2008
Elliptic solitons, Fuchsian equations, and algorithms. Zbl 1276.35052
Brezhnev, Yu. V.
2013
On uniformization of algebraic curves. Zbl 1167.30018
Brezhnev, Yu. V.
2008
On the $$\Psi$$-function for finite-gap potentials. Zbl 1098.34580
Ustinov, N. V.; Brezhnev, Yu. V.
2002
Darboux transformation, positons and general superposition formula for the sine-Gordon equation. Zbl 1020.35517
Andreev, V. A.; Brezhnev, Yu. V.
1995
On uniformization of Burnside’s curve $$y^2 = x^5 - x$$. Zbl 1283.30070
Brezhnev, Yu. V.
2009
Elliptic solitons and Gröbner bases. Zbl 1070.37050
Brezhnev, Yurii V.
2004
The sixth Painlevé transcendent and uniformization of algebraic curves. Zbl 1345.34145
Brezhnev, Yurii V.
2016
The mean values of the Weierstrass elliptic function $$\wp$$: theory and application. Zbl 1293.33023
Sherratt, Jonathan A.; Brezhnev, Yurii V.
2013
A note on Chudnovsky’s Fuchsian equations. Zbl 1264.34173
Brezhnev, Yurii V.
2012
Dynamical systems defining Jacobi’s $$\theta$$-constants. Zbl 1272.37030
Brezhnev, Yurii V.; Lyakhovich, Simon L.; Sharapov, Alexey A.
2011
On Dubrovin equations for finite-gap operators. Zbl 1098.34579
Brezhnev, Yu. V.
2002
Elliptic solitons with free constants and their isospectral deformations. Zbl 1011.37044
Brezhnev, Yurii V.
2001
The sixth Painlevé transcendent and uniformization of algebraic curves. Zbl 1345.34145
Brezhnev, Yurii V.
2016
Non-canonical extension of $$\theta$$-functions and modular integrability of $$\vartheta$$-constants. Zbl 1318.33034
Brezhnev, Yurii V.
2013
Elliptic solitons, Fuchsian equations, and algorithms. Zbl 1276.35052
Brezhnev, Yu. V.
2013
The mean values of the Weierstrass elliptic function $$\wp$$: theory and application. Zbl 1293.33023
Sherratt, Jonathan A.; Brezhnev, Yurii V.
2013
Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials. Zbl 1248.81032
Brezhnev, Yurii V.
2012
A note on Chudnovsky’s Fuchsian equations. Zbl 1264.34173
Brezhnev, Yurii V.
2012
Dynamical systems defining Jacobi’s $$\theta$$-constants. Zbl 1272.37030
Brezhnev, Yurii V.; Lyakhovich, Simon L.; Sharapov, Alexey A.
2011
A $$\tau$$-function solution of the sixth Painlevé transcendent. Zbl 1185.37137
Brezhnev, Yu. V.
2009
On uniformization of Burnside’s curve $$y^2 = x^5 - x$$. Zbl 1283.30070
Brezhnev, Yu. V.
2009
What does integrability of finite-gap or soliton potentials mean? Zbl 1153.37411
Brezhnev, Yurii V.
2008
On uniformization of algebraic curves. Zbl 1167.30018
Brezhnev, Yu. V.
2008
Elliptic solitons and Gröbner bases. Zbl 1070.37050
Brezhnev, Yurii V.
2004
Finite-gap potentials with trigonal curves. Zbl 1087.34561
Brezhnev, Yu. V.
2002
On the $$\Psi$$-function for finite-gap potentials. Zbl 1098.34580
Ustinov, N. V.; Brezhnev, Yu. V.
2002
On Dubrovin equations for finite-gap operators. Zbl 1098.34579
Brezhnev, Yu. V.
2002
Elliptic solitons with free constants and their isospectral deformations. Zbl 1011.37044
Brezhnev, Yurii V.
2001
Darboux transformation and some multi-phase solutions of the Dodd-Bullough-Tzitzeica equation: $$U_{xt}=e^ U-e^{-2U}$$. Zbl 1072.35555
Brezhnev, Yurii V.
1996
Darboux transformation, positons and general superposition formula for the sine-Gordon equation. Zbl 1020.35517
Andreev, V. A.; Brezhnev, Yu. V.
1995
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#### Cited by 54 Authors

 17 Geng, Xianguo 8 He, Guoliang 8 Zeng, Xin 7 Brezhnev, Yurii V. 6 Wu, Lihua 5 Wei, Jiao 4 Chen, Zhijie 4 Lin, Chang-Shou 4 Morales-Ruiz, Juan José 3 Kuo, Ting-Jung 3 Zhai, Yunyun 3 Zurro, María-Angeles 2 Guzzetti, Davide 2 Jiménez, Sonia 2 Sánchez-Cauce, Raquel 2 Smirnov, Alexander O. 1 Bertrand, Sébastien 1 Blower, Gordon 1 Bruno, Alexander Dmitrievich 1 Combot, Thierry 1 Conte, Robert M. 1 Sobreira de Araujo Corrêa, Francisco Julio 1 Dai, Hui-Hui 1 El-Kalaawy, Omar H. 1 Esmakhanova, Kuralay 1 Gontsov, Renat R. 1 Goryuchkina, Irina V. 1 Grundland, Alfred Michel 1 Guttmann, Anthony John 1 He, Lin 1 Lechtenfeld, Olaf 1 Maevskii, E. V. 1 Mangazeev, Vladimir V. 1 Matveev, Vladimir B. 1 Musette, Micheline 1 Myrzakulov, Ratbay 1 Myrzakulov, Yerlan 1 Nimmo, Jonathan J. C. 1 Nugmanova, Gulgasyl Nukarbaevna 1 Papathanasiou, Georgios 1 Plyushchay, Mikhail S. 1 Popov, A. G. 1 Rueda, Sonia L. 1 Rui, Weiguo 1 Ruijsenaars, Simon N. M. 1 Sazonov, Sergey V. 1 Shen, Guicheng 1 Sherratt, Jonathan A. 1 Sun, Yunchuan 1 Ustinov, Nikolai V. 1 Xiong, Yongping 1 Xue, Bo 1 Zhang, Mei 1 Zhang, Wenling
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#### Cited in 35 Serials

 7 Journal of Geometry and Physics 6 Journal of Mathematical Physics 5 Theoretical and Mathematical Physics 2 Chaos, Solitons and Fractals 2 Physica D 2 Journal of High Energy Physics 2 Journal of Applied Mathematics 1 Applicable Analysis 1 Communications in Mathematical Physics 1 International Journal of Theoretical Physics 1 Journal of Mathematical Analysis and Applications 1 Letters in Mathematical Physics 1 Mathematical Notes 1 Nuclear Physics. B 1 Reports on Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Reviews in Mathematical Physics 1 Advances in Mathematics 1 Journal of Differential Equations 1 Transactions of the American Mathematical Society 1 Advances in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Constructive Approximation 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Nonlinear Science 1 Journal of Mathematical Sciences (New York) 1 St. Petersburg Mathematical Journal 1 Annales Henri Poincaré 1 Computational Methods and Function Theory 1 Advances in Difference Equations 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Journal of Zhejiang University. Science A 1 Journal of Physics A: Mathematical and Theoretical 1 Science China. Mathematics 1 Analysis and Mathematical Physics
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#### Cited in 21 Fields

 33 Dynamical systems and ergodic theory (37-XX) 21 Partial differential equations (35-XX) 17 Algebraic geometry (14-XX) 14 Ordinary differential equations (34-XX) 6 Quantum theory (81-XX) 4 Field theory and polynomials (12-XX) 4 Functions of a complex variable (30-XX) 4 Special functions (33-XX) 3 Number theory (11-XX) 3 Operator theory (47-XX) 2 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX)