Compute Distance To:
 Documents Indexed: 60 Publications since 1989 Co-Authors: 40 Co-Authors with 35 Joint Publications 1,355 Co-Co-Authors
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### Co-Authors

 24 single-authored 13 Shabat, Alekseĭ Borisovich 6 Khabibullin, Ismagil Talgatovich 6 Suris, Yuri Borisovich 5 Bobenko, Alexander Ivanovich 4 Postnikov, V. V. 3 Sokolov, Vladimir Vyacheslavovich 3 Yamilov, Ravil Islamovich 2 Ferapontov, Evgeny Vladimirovich 2 Marikhin, Vladimir G. 1 Askhabov, Sultan Nazhmudinovich 1 Berest, Yuri Yu. 1 Bukhshtaber, Viktor Matveevich 1 Chalykh, Oleg A. 1 Cherdantsev, I. Yu. 1 Dubrovin, Boris Anatol’evich 1 Etingof, Pavel Il’ich 1 Feigin, Misha V. 1 Felder, J. 1 Fordy, Allan P. 1 Garifullin, Rustem N. 1 Grinevich, Pëtr Georgievich 1 Gürel, Burak 1 Gürses, Metin 1 Krichever, Igor’ Moiseevich 1 Kulaev, Ruslan Chermenovich 1 Kusraev, Anatoly Georgievich 1 Kutateladze, Semën Samsonovich 1 Mikhailov, Alexander Vasil’evich 1 Musin, Il’dar Khamitovich 1 Nijhoff, Frank W. 1 Novikov, Sergeĭ Petrovich 1 Pogrebkov, Andrei K. 1 Reshetnyak, Yuriĭ Grigor’evich 1 Sergeev, Aleksandr Nikolaevich 1 Suleĭmanov, Bulat Irekovich 1 Svinolupov, S. I. 1 Veselov, Alexander Petrovich 1 Vinternitz, P. 1 Yulmukhametov, Rinad Salavatovich 1 Zhiber, Anatoliĭ Vasil’evich
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### Serials

 19 Theoretical and Mathematical Physics 7 Journal of Physics A: Mathematical and Theoretical 5 Functional Analysis and its Applications 4 Journal of Physics A: Mathematical and General 3 Physics Letters. A 3 IMRN. International Mathematics Research Notices 2 Physica D 2 Journal of Nonlinear Mathematical Physics 2 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Communications in Mathematical Physics 1 Letters in Mathematical Physics 1 Russian Mathematical Surveys 1 Acta Applicandae Mathematicae 1 Journal of Symbolic Computation 1 Discrete & Computational Geometry 1 Communications in Analysis and Geometry 1 Mathematical Physics, Analysis and Geometry 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
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### Fields

 45 Dynamical systems and ergodic theory (37-XX) 28 Partial differential equations (35-XX) 10 Ordinary differential equations (34-XX) 8 Difference and functional equations (39-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Quantum theory (81-XX) 3 History and biography (01-XX) 3 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 Mechanics of particles and systems (70-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Numerical analysis (65-XX)

### Citations contained in zbMATH Open

48 Publications have been cited 651 times in 415 Documents Cited by Year
Classification of integrable equations on quad-graphs. The consistency approach. Zbl 1075.37022
Adler, V. E.; Bobenko, A. I.; Suris, Yu. B.
2003
Discrete nonlinear hyperbolic equations. Classification of integrable cases. Zbl 1271.37048
Adler, V. E.; Bobenko, A. I.; Suris, Yu. B.
2009
Symmetry approach to the integrability problem. Zbl 1029.37041
Adler, V. E.; Shabat, A. B.; Yamilov, R. I.
2000
A modification of Crum’s method. Zbl 0857.34069
1994
Nonlinear chains and Painlevé equations. Zbl 0812.34030
1994
Discrete analogues of the Liouville equation. Zbl 0987.37066
Adler, V. E.; Startsev, S. Ya.
1999
Multi-component Volterra and Toda type integrable equations. Zbl 0983.37082
Adler, V. E.; Svinolupov, S. I.; Yamilov, R. I.
1999
Geometry of Yang-Baxter maps: pencils of conics and quadrirational mappings. Zbl 1065.14015
Adler, V. E.; Bobenko, A. I.; Suris, Yu. B.
2004
Recuttings of polygons. Zbl 0812.58072
1993
$$\text{Q}_4$$: Integrable master equation related to an elliptic curve. Zbl 1081.37038
Adler, V. E.; Suris, Yu. B.
2004
Bäcklund transformation for the Krichever-Novikov equation. Zbl 0895.35089
1998
Boundary conditions for integrable equations. Zbl 0927.35093
Adler, V.; Gürel, B.; Gürses, M.; Habibullin, I.
1997
Explicit auto-transformations of integrable chains. Zbl 0826.35115
Adler, V. E.; Yamilov, R. I.
1994
Model equation of the theory of solitons. Zbl 1138.37044
Adler, V. È.; Shabat, A. B.
2007
On vector analogs of the modified Volterra lattice. Zbl 1157.35464
Adler, V. E.; Postnikov, V. V.
2008
Classification of integrable discrete equations of octahedron type. Zbl 1277.39006
Adler, Vsevolod E.; Bobenko, Alexander I.; Suris, Yuri B.
2012
On a class of Toda chains. Zbl 0978.37502
Adler, V. E.; Shabat, A. B.
1997
Generalized Legendre transformations. Zbl 0978.37504
Adler, V. E.; Shabat, A. B.
1997
Discrete equations on planar graphs. Zbl 1001.37081
2001
Lagrangian chains and canonical Bäcklund transformations. Zbl 1029.37042
Adler, V. E.; Marikhin, V. G.; Shabat, A. B.
2001
Differential-difference equations associated with the fractional Lax operators. Zbl 1230.34013
Adler, V. E.; Postnikov, V. V.
2011
Integrable Möbius-invariant evolutionary lattices of second order. Zbl 1364.35399
2016
Necessary integrability conditions for evolutionary lattice equations. Zbl 1330.34028
2014
On discrete 2D integrable equations of higher order. Zbl 1301.37037
Adler, V. E.; Postnikov, V. V.
2014
Legendre transforms on a triangular lattice. Zbl 0976.37043
2000
Boundary value problem for the KdV equation on a half-line. Zbl 0916.35100
Adler, V. E.; Habibullin, I. T.; Shabat, A. B.
1997
Integrable deformations of a polygon. Zbl 1194.35353
1995
Integrable boundary conditions for the Toda lattice. Zbl 0872.58033
Adler, V. E.; Habibullin, I. T.
1995
Discretizations of the Landau-Lifshits equation. Zbl 0984.39010
2000
Toward a theory of integrable hyperbolic equations of third order. Zbl 1297.37030
Adler, V. E.; Shabat, A. B.
2012
On the structure of the Bäcklund transformations for the relativistic lattices. Zbl 1119.37330
2000
Integrability test for evolutionary lattice equations of higher order. Zbl 1329.65311
2016
Cauchy problem for integrable discrete equations on quad-graphs. Zbl 1067.37086
Adler, V. E.; Veselov, A. P.
2004
Integrable seven-point discrete equations and second-order evolution chains. Zbl 1401.37072
2018
Nonlinear superposition principle for the Jordan NLS equation. Zbl 0959.35509
1994
Classification of integrable Volterra-type lattices on the sphere: Isotropic case. Zbl 1166.35034
2008
Boundary conditions for integrable lattices. Zbl 0912.35145
Adler, V. E.; Habibullin, I. T.
1997
Non-abelian evolution systems with conservation laws. Zbl 1467.37059
Adler, V. E.; Sokolov, V. V.
2021
On the rational solutions of the Shabat equation. Zbl 0941.34515
1996
On the one class of hyperbolic systems. Zbl 1138.35360
Adler, Vsevolod E.; Shabat, Alexey B.
2006
Integrable discrete nets in Grassmannians. Zbl 1181.37109
Adler, Vsevolod Eduardovich; Bobenko, Alexander Ivanovich; Suris, Yuri Borisovich
2009
First integrals of generalized Toda chains. Zbl 0981.37029
Adler, V. È.; Shabat, A. B.
1998
On the N-soliton solution of the Korteweg-de Vries equation. Zbl 0741.35063
1989
Nonautonomous symmetries of the KdV equation and step-like solutions. Zbl 1436.35284
2020
Some incidence theorems and integrable discrete equations. Zbl 1103.51002
2006
The tangential map and associated integrable equations. Zbl 1181.37093
2009
Dressing chain for the acoustic spectral problem. Zbl 1177.37063
Adler, V. E.; Shabat, A. B.
2006
Matrix Painlevé II equations. Zbl 1471.34168
Adler, V. E.; Sokolov, V. V.
2021
Non-abelian evolution systems with conservation laws. Zbl 1467.37059
Adler, V. E.; Sokolov, V. V.
2021
Matrix Painlevé II equations. Zbl 1471.34168
Adler, V. E.; Sokolov, V. V.
2021
Nonautonomous symmetries of the KdV equation and step-like solutions. Zbl 1436.35284
2020
Integrable seven-point discrete equations and second-order evolution chains. Zbl 1401.37072
2018
Integrable Möbius-invariant evolutionary lattices of second order. Zbl 1364.35399
2016
Integrability test for evolutionary lattice equations of higher order. Zbl 1329.65311
2016
Necessary integrability conditions for evolutionary lattice equations. Zbl 1330.34028
2014
On discrete 2D integrable equations of higher order. Zbl 1301.37037
Adler, V. E.; Postnikov, V. V.
2014
Classification of integrable discrete equations of octahedron type. Zbl 1277.39006
Adler, Vsevolod E.; Bobenko, Alexander I.; Suris, Yuri B.
2012
Toward a theory of integrable hyperbolic equations of third order. Zbl 1297.37030
Adler, V. E.; Shabat, A. B.
2012
Differential-difference equations associated with the fractional Lax operators. Zbl 1230.34013
Adler, V. E.; Postnikov, V. V.
2011
Discrete nonlinear hyperbolic equations. Classification of integrable cases. Zbl 1271.37048
Adler, V. E.; Bobenko, A. I.; Suris, Yu. B.
2009
Integrable discrete nets in Grassmannians. Zbl 1181.37109
Adler, Vsevolod Eduardovich; Bobenko, Alexander Ivanovich; Suris, Yuri Borisovich
2009
The tangential map and associated integrable equations. Zbl 1181.37093
2009
On vector analogs of the modified Volterra lattice. Zbl 1157.35464
Adler, V. E.; Postnikov, V. V.
2008
Classification of integrable Volterra-type lattices on the sphere: Isotropic case. Zbl 1166.35034
2008
Model equation of the theory of solitons. Zbl 1138.37044
Adler, V. È.; Shabat, A. B.
2007
On the one class of hyperbolic systems. Zbl 1138.35360
Adler, Vsevolod E.; Shabat, Alexey B.
2006
Some incidence theorems and integrable discrete equations. Zbl 1103.51002
2006
Dressing chain for the acoustic spectral problem. Zbl 1177.37063
Adler, V. E.; Shabat, A. B.
2006
Geometry of Yang-Baxter maps: pencils of conics and quadrirational mappings. Zbl 1065.14015
Adler, V. E.; Bobenko, A. I.; Suris, Yu. B.
2004
$$\text{Q}_4$$: Integrable master equation related to an elliptic curve. Zbl 1081.37038
Adler, V. E.; Suris, Yu. B.
2004
Cauchy problem for integrable discrete equations on quad-graphs. Zbl 1067.37086
Adler, V. E.; Veselov, A. P.
2004
Classification of integrable equations on quad-graphs. The consistency approach. Zbl 1075.37022
Adler, V. E.; Bobenko, A. I.; Suris, Yu. B.
2003
Discrete equations on planar graphs. Zbl 1001.37081
2001
Lagrangian chains and canonical Bäcklund transformations. Zbl 1029.37042
Adler, V. E.; Marikhin, V. G.; Shabat, A. B.
2001
Symmetry approach to the integrability problem. Zbl 1029.37041
Adler, V. E.; Shabat, A. B.; Yamilov, R. I.
2000
Legendre transforms on a triangular lattice. Zbl 0976.37043
2000
Discretizations of the Landau-Lifshits equation. Zbl 0984.39010
2000
On the structure of the Bäcklund transformations for the relativistic lattices. Zbl 1119.37330
2000
Discrete analogues of the Liouville equation. Zbl 0987.37066
Adler, V. E.; Startsev, S. Ya.
1999
Multi-component Volterra and Toda type integrable equations. Zbl 0983.37082
Adler, V. E.; Svinolupov, S. I.; Yamilov, R. I.
1999
Bäcklund transformation for the Krichever-Novikov equation. Zbl 0895.35089
1998
First integrals of generalized Toda chains. Zbl 0981.37029
Adler, V. È.; Shabat, A. B.
1998
Boundary conditions for integrable equations. Zbl 0927.35093
Adler, V.; Gürel, B.; Gürses, M.; Habibullin, I.
1997
On a class of Toda chains. Zbl 0978.37502
Adler, V. E.; Shabat, A. B.
1997
Generalized Legendre transformations. Zbl 0978.37504
Adler, V. E.; Shabat, A. B.
1997
Boundary value problem for the KdV equation on a half-line. Zbl 0916.35100
Adler, V. E.; Habibullin, I. T.; Shabat, A. B.
1997
Boundary conditions for integrable lattices. Zbl 0912.35145
Adler, V. E.; Habibullin, I. T.
1997
On the rational solutions of the Shabat equation. Zbl 0941.34515
1996
Integrable deformations of a polygon. Zbl 1194.35353
1995
Integrable boundary conditions for the Toda lattice. Zbl 0872.58033
Adler, V. E.; Habibullin, I. T.
1995
A modification of Crum’s method. Zbl 0857.34069
1994
Nonlinear chains and Painlevé equations. Zbl 0812.34030
1994
Explicit auto-transformations of integrable chains. Zbl 0826.35115
Adler, V. E.; Yamilov, R. I.
1994
Nonlinear superposition principle for the Jordan NLS equation. Zbl 0959.35509
1994
Recuttings of polygons. Zbl 0812.58072
1993
On the N-soliton solution of the Korteweg-de Vries equation. Zbl 0741.35063
1989
all top 5

### Cited by 366 Authors

 19 Adler, Vsevolod Eduardovich 19 Khabibullin, Ismagil Talgatovich 16 Zhang, Dajun 12 Mikhailov, Alexander Vasil’evich 11 Shabat, Alekseĭ Borisovich 11 Suris, Yuri Borisovich 11 Yamilov, Ravil Islamovich 10 Joshi, Nalini 10 Nijhoff, Frank W. 10 Wang, Jingping 9 Gómez-Ullate, David 9 Milson, Robert 9 Odake, Satoru 8 Bobenko, Alexander Ivanovich 8 Gubbiotti, Giorgio 8 Nakazono, Nobutaka 8 Xenitidis, Pavlos 7 Doliwa, Adam 7 Kassotakis, Pavlos G. 7 Levi, Decio 7 Sasaki, Ryu 7 Zheltukhina, Natalya A. 6 Clarkson, Peter A. 6 Grandati, Yves 6 Nieszporski, Maciej 6 van der Kamp, Peter H. 6 Zhang, Danda 6 Zhao, Songlin 6 Zheltukhin, Kostyantyn 5 Boll, Raphael 5 Ferapontov, Evgeny Vladimirovich 5 Grammaticos, Basil 5 Kels, Andrew P. 5 Morozov, Oleg I. 5 Quispel, Gilles Reinout Willem 5 Ramani, Alfred 5 Scimiterna, Christian 5 Vereshchagin, V. L. 4 Atkinson, James R. 4 Durán, Antonio José 4 Hone, Andrew N. W. 4 Hydon, Peter Ellsworth 4 Konstantinou-Rizos, Sotiris 4 Marquette, Ian 4 Papageorgiou, Vassilios G. 4 Poptsova, Mariya Nikolaevna 4 Sahadevan, Ramajayam 4 Sergeev, Sergeĭ Mikhaĭlovich 4 Tabachnikov, Serge L. 4 Tran, Dinh Thi 4 Vakhnenko, Oleksiy O. 4 Veselov, Alexander Petrovich 4 Zharinov, Victor Victorovich 3 Bazhanov, Vladimir V. 3 Dragović, Vladimir 3 Fordy, Allan P. 3 Ignat’ev, Mikhail Yur’evich 3 Kouloukas, Theodoros E. 3 Lobb, Sarah B. 3 Marikhin, Vladimir G. 3 Nagavigneshwari, G. 3 Nagoya, Hajime 3 Novikov, Vladimir S. 3 Papamikos, Georgios A. 3 Peng, Linyu 3 Petrera, Matteo 3 Quesne, Christiane 3 Rasin, Alexander G. 3 Schief, Wolfgang Karl 3 Schiff, Jeremy 3 Sergyeyev, Artur 3 Shemyakova, Ekaterina 3 Shi, Yang 3 Smirnov, Sergei Valer’evich 3 Sokolov, Vladimir Vyacheslavovich 3 Tongas, Anastasios G. 3 Tsuda, Teruhisa 3 Vekslerchik, Vadym Yevgenovych 3 Viallet, Claude Michel 3 Wang, Zhen 3 Yamazaki, Masahito 3 Zhu, Zuonong 2 Akopyan, Arseniy V. 2 Avan, Jean 2 Balakhnev, M. Yu. 2 Baran, Hynek 2 Boutet de Monvel, Anne Marie 2 Cao, Cewen 2 Carpentier, Sylvain 2 Casati, Matteo 2 Demskoi, Dmitry K. 2 Dubrovsky, V. G. 2 Evripidou, Charalampos A. 2 Fan, Engui 2 Filipuk, Galina V. 2 Forrester, Peter J. 2 Fu, Wei 2 García-Ferrero, Maria Ángeles 2 Garifullin, Rustem Nailevich 2 Gordoa, Pilar Ruiz ...and 266 more Authors
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### Cited in 95 Serials

 57 Theoretical and Mathematical Physics 53 Journal of Mathematical Physics 37 Journal of Nonlinear Mathematical Physics 21 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 18 Letters in Mathematical Physics 15 Journal of Physics A: Mathematical and Theoretical 12 Communications in Mathematical Physics 11 Ufimskiĭ Matematicheskiĭ Zhurnal 7 Applied Mathematics and Computation 7 Mathematical Physics, Analysis and Geometry 7 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 6 Physics Letters. A 6 Studies in Applied Mathematics 6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 5 Nonlinearity 5 Nuclear Physics. B 5 Functional Analysis and its Applications 5 Journal of Approximation Theory 5 Communications in Nonlinear Science and Numerical Simulation 4 Journal of Geometry and Physics 4 Physica D 4 International Journal of Mathematics 3 Journal of Mathematical Analysis and Applications 3 Reports on Mathematical Physics 3 Advances in Mathematics 3 Applied Mathematics Letters 3 Journal of Difference Equations and Applications 3 Foundations of Computational Mathematics 3 Advances in Difference Equations 3 Frontiers of Mathematics in China 3 Journal of Computational Dynamics 2 Applicable Analysis 2 Computers & Mathematics with Applications 2 Mathematical Notes 2 Russian Mathematical Surveys 2 Inventiones Mathematicae 2 Proceedings of the American Mathematical Society 2 Discrete & Computational Geometry 2 Journal of Nonlinear Science 2 Journal of Mathematical Sciences (New York) 2 St. Petersburg Mathematical Journal 2 Abstract and Applied Analysis 2 Regular and Chaotic Dynamics 2 Lobachevskii Journal of Mathematics 2 Journal of Statistical Mechanics: Theory and Experiment 1 Modern Physics Letters A 1 Modern Physics Letters B 1 International Journal of Modern Physics A 1 Bulletin of the Australian Mathematical Society 1 Communications on Pure and Applied Mathematics 1 International Journal of Theoretical Physics 1 Journal of Statistical Physics 1 Mathematical Methods in the Applied Sciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physics Reports 1 Wave Motion 1 Chaos, Solitons and Fractals 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of Differential Equations 1 Journal of the London Mathematical Society. Second Series 1 Mathematics and Computers in Simulation 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Siberian Mathematical Journal 1 Transactions of the American Mathematical Society 1 Acta Applicandae Mathematicae 1 Journal of Symbolic Computation 1 Japan Journal of Industrial and Applied Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Indagationes Mathematicae. New Series 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Integral Transforms and Special Functions 1 Nonlinear Dynamics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Discrete Dynamics in Nature and Society 1 Journal of High Energy Physics 1 Annales Henri Poincaré 1 Differential Equations 1 Journal of Systems Science and Complexity 1 Journal of Applied Mathematics 1 Computational Methods and Function Theory 1 International Journal of Geometric Methods in Modern Physics 1 Complex Variables and Elliptic Equations 1 Proceedings of the Steklov Institute of Mathematics 1 Groups, Geometry, and Dynamics 1 The Annals of Applied Statistics 1 Journal of Geometric Mechanics 1 Science China. Mathematics 1 Symmetry 1 Random Matrices: Theory and Applications 1 Analysis and Mathematical Physics 1 Annalen der Physik 1 Arnold Mathematical Journal 1 Journal of Elliptic and Parabolic Equations 1 Proceedings of the American Mathematical Society. Series B
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### Cited in 43 Fields

 262 Dynamical systems and ergodic theory (37-XX) 144 Partial differential equations (35-XX) 132 Difference and functional equations (39-XX) 79 Ordinary differential equations (34-XX) 52 Special functions (33-XX) 52 Quantum theory (81-XX) 22 Associative rings and algebras (16-XX) 19 Nonassociative rings and algebras (17-XX) 19 Mechanics of particles and systems (70-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 16 Statistical mechanics, structure of matter (82-XX) 14 Differential geometry (53-XX) 13 Algebraic geometry (14-XX) 13 Numerical analysis (65-XX) 11 Geometry (51-XX) 11 Convex and discrete geometry (52-XX) 10 Global analysis, analysis on manifolds (58-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 6 Number theory (11-XX) 6 Functions of a complex variable (30-XX) 6 Operator theory (47-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Functional analysis (46-XX) 3 Computer science (68-XX) 2 Integral transforms, operational calculus (44-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX)