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 Documents Indexed: 57 Publications since 1989
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Co-Authors

 23 single-authored 13 Shabat, Alekseĭ Borisovich 6 Khabibullin, Ismagil Talgatovich 6 Suris, Yuri Borisovich 5 Bobenko, Alexander Ivanovich 4 Postnikov, V. V. 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 Fordi, A. 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 Levi, Dan 1 Mikhailov, Alexander Vasil’evich 1 Musin, Il’dar Khamitovich 1 Niĭkhof, F. W. 1 Novikov, Sergeĭ Petrovich 1 Pogrebkov, Andrei K. 1 Reshetnyak, Yuriĭ Grigor’evich 1 Sergeev, Aleksandr Nikolaevich 1 Sharipov, Ruslan A. 1 Sokolov, Vladimir Vyacheslavovich 1 Startsev, Sergeĭ Yakovlevich 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

 18 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 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 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Ufimskiĭ Matematicheskiĭ Zhurnal
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Fields

 43 Dynamical systems and ergodic theory (37-XX) 27 Partial differential equations (35-XX) 9 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

45 Publications have been cited 571 times in 364 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
Symmetry approach to the integrability problem. Zbl 1029.37041
Adler, V. E.; Shabat, A. B.; Yamilov, R. I.
2000
Discrete nonlinear hyperbolic equations. Classification of integrable cases. Zbl 1271.37048
Adler, V. E.; Bobenko, A. I.; Suris, Yu. B.
2009
A modification of Crum’s method. Zbl 0857.34069
1994
Nonlinear chains and Painlevé equations. Zbl 0812.34030
1994
Multi-component Volterra and Toda type integrable equations. Zbl 0983.37082
Adler, V. E.; Svinolupov, S. I.; Yamilov, R. I.
1999
Recuttings of polygons. Zbl 0812.58072
1993
Geometry of Yang-Baxter maps: pencils of conics and quadrirational mappings. Zbl 1065.14015
Adler, V. E.; Bobenko, A. I.; Suris, Yu. B.
2004
Discrete analogues of the Liouville equation. Zbl 0987.37066
Adler, V. E.; Startsev, S. Ya.
1999
$$\text{Q}_4$$: 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
On vector analogs of the modified Volterra lattice. Zbl 1157.35464
Adler, V. E.; Postnikov, V. V.
2008
Model equation of the theory of solitons. Zbl 1138.37044
Adler, V. È.; Shabat, A. B.
2007
Classification of integrable discrete equations of octahedron type. Zbl 1277.39006
Adler, Vsevolod E.; Bobenko, Alexander I.; Suris, Yuri B.
2012
Generalized Legendre transformations. Zbl 0978.37504
Adler, V. E.; Shabat, A. B.
1997
On a class of Toda chains. Zbl 0978.37502
Adler, V. E.; Shabat, A. B.
1997
Lagrangian chains and canonical Bäcklund transformations. Zbl 1029.37042
Adler, V. E.; Marikhin, V. G.; Shabat, A. B.
2001
Discrete equations on planar graphs. Zbl 1001.37081
2001
Integrable Möbius-invariant evolutionary lattices of second order. Zbl 1364.35399
2016
Differential-difference equations associated with the fractional Lax operators. Zbl 1230.34013
Adler, V. E.; Postnikov, V. V.
2011
Legendre transforms on a triangular lattice. Zbl 0976.37043
2000
Integrable deformations of a polygon. Zbl 1194.35353
1995
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
Toward a theory of integrable hyperbolic equations of third order. Zbl 1297.37030
Adler, V. E.; Shabat, A. B.
2012
Discretizations of the Landau-Lifshits equation. Zbl 0984.39010
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 boundary conditions for the Toda lattice. Zbl 0872.58033
Adler, V. E.; Habibullin, I. T.
1995
Cauchy problem for integrable discrete equations on quad-graphs. Zbl 1067.37086
Adler, V. E.; Veselov, A. P.
2004
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
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
Integrable seven-point discrete equations and second-order evolution chains. Zbl 1401.37072
2018
Integrable discrete nets in Grassmannians. Zbl 1181.37109
Adler, Vsevolod Eduardovich; Bobenko, Alexander Ivanovich; Suris, Yuri Borisovich
2009
On the one class of hyperbolic systems. Zbl 1138.35360
Adler, Vsevolod E.; Shabat, Alexey B.
2006
On the rational solutions of the Shabat equation. Zbl 0941.34515
1996
Nonlinear superposition principle for the Jordan NLS equation. Zbl 0959.35509
1994
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
Some incidence theorems and integrable discrete equations. Zbl 1103.51002
2006
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
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
Dressing chain for the acoustic spectral problem. Zbl 1177.37063
Adler, V. E.; Shabat, A. B.
2006
Some incidence theorems and integrable discrete equations. Zbl 1103.51002
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
Lagrangian chains and canonical Bäcklund transformations. Zbl 1029.37042
Adler, V. E.; Marikhin, V. G.; Shabat, A. B.
2001
Discrete equations on planar graphs. Zbl 1001.37081
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
Multi-component Volterra and Toda type integrable equations. Zbl 0983.37082
Adler, V. E.; Svinolupov, S. I.; Yamilov, R. I.
1999
Discrete analogues of the Liouville equation. Zbl 0987.37066
Adler, V. E.; Startsev, S. Ya.
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
Generalized Legendre transformations. Zbl 0978.37504
Adler, V. E.; Shabat, A. B.
1997
On a class of Toda chains. Zbl 0978.37502
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 342 Authors

 19 Khabibullin, Ismagil Talgatovich 16 Adler, Vsevolod Eduardovich 15 Zhang, Dajun 11 Mikhailov, Alexander Vasil’evich 11 Shabat, Alekseĭ Borisovich 11 Suris, Yuri Borisovich 10 Yamilov, Ravil Islamovich 9 Joshi, Nalini 9 Nijhoff, Frank W. 9 Odake, Satoru 8 Bobenko, Alexander Ivanovich 8 Wang, Jingping 8 Xenitidis, Pavlos 7 Gómez-Ullate, David 7 Gubbiotti, Giorgio 7 Kassotakis, Pavlos G. 7 Milson, Robert 6 Clarkson, Peter A. 6 Doliwa, Adam 6 Garifullin, Rustem Nailevich 6 Levi, Decio 6 Nakazono, Nobutaka 6 Nieszporski, Maciej 6 Sasaki, Ryu 6 Zhao, Songlin 6 Zheltukhina, Natalya A. 5 Boll, Raphael 5 Grammaticos, Basil 5 Morozov, Oleg I. 5 Quispel, Gilles Reinout Willem 5 Ramani, Alfred 5 Scimiterna, Christian 5 van der Kamp, Peter H. 5 Vereshchagin, V. L. 5 Zhang, Danda 5 Zheltukhin, Kostyantyn 4 Atkinson, James R. 4 Duran, Antonio J. 4 Ferapontov, Evgeny Vladimirovich 4 Grandati, Yves 4 Hone, Andrew N. W. 4 Hydon, Peter Ellsworth 4 Marquette, Ian 4 Papageorgiou, Vassilios G. 4 Poptsova, Mariya Nikolaevna 4 Sahadevan, Ramajayam 4 Smirnov, Sergei Valer’evich 4 Tabachnikov, Serge L. 4 Tran, Dinh Thi 4 Vakhnenko, Oleksiy O. 4 Veselov, Alexander Petrovich 4 Zharinov, Victor Victorovich 3 Dragović, Vladimir 3 Fordy, Allan P. 3 Garifullin, Rustem N. 3 Hietarinta, Jarmo 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 Peng, Linyu 3 Petrera, Matteo 3 Quesne, Christiane 3 Rasin, Alexander G. 3 Schiff, Jeremy 3 Sergeev, Sergeĭ Mikhaĭlovich 3 Sergyeyev, Artur 3 Shemyakova, Ekaterina 3 Shi, Yang 3 Tongas, Anastasios G. 3 Tsuda, Teruhisa 3 Vekslerchik, Vadym Yevgenovych 3 Wang, Zhen 3 Zhu, Zuonong 2 Akopyan, Arseniy V. 2 Avan, Jean 2 Balakhnev, Maxim Ju. 2 Baran, Hynek 2 Bazhanov, Vladimir V. 2 Boutet de Monvel, Anne Marie 2 Carpentier, Sylvain 2 Evripidou, Charalampos A. 2 Fan, Engui 2 Filipuk, Galina V. 2 Forrester, Peter J. 2 García-Ferrero, Maria Ángeles 2 Gürses, Metin 2 Hereman, Willy A. 2 Kajiwara, Kenji 2 Kamran, Niky 2 Kels, Andrew P. 2 Khakimova, Aĭgul’ Rinatovna 2 Khusnutdinova, Karima Robertovna 2 Konstantinou-Rizos, Sotiris 2 Krasil’shchik, Iosif Semënovich 2 Miki, Hiroshi 2 Novikov, Vladimir S. 2 Papamikos, Georgios A. ...and 242 more Authors
all top 5

Cited in 86 Serials

 53 Theoretical and Mathematical Physics 52 Journal of Mathematical Physics 37 Journal of Nonlinear Mathematical Physics 18 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 16 Letters in Mathematical Physics 15 Journal of Physics A: Mathematical and Theoretical 10 Communications in Mathematical Physics 6 Journal of Geometry and Physics 6 Applied Mathematics and Computation 6 Studies in Applied Mathematics 6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 5 Physics Letters. A 5 Functional Analysis and its Applications 5 Journal of Approximation Theory 5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 4 Nuclear Physics. B 4 International Journal of Mathematics 4 Communications in Nonlinear Science and Numerical Simulation 4 Ufimskiĭ Matematicheskiĭ Zhurnal 3 Journal of Mathematical Analysis and Applications 3 Nonlinearity 3 Journal of Difference Equations and Applications 3 Mathematical Physics, Analysis and Geometry 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 Reports on Mathematical Physics 2 Advances in Mathematics 2 Inventiones Mathematicae 2 Proceedings of the American Mathematical Society 2 Discrete & Computational Geometry 2 Applied Mathematics Letters 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 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 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 Physica D 1 Journal of Symbolic Computation 1 Japan Journal of Industrial and Applied Mathematics 1 Bulletin of the American Mathematical Society. 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 The Annals of Applied Statistics 1 Journal of Geometric Mechanics 1 Science China. Mathematics 1 Symmetry 1 Random Matrices: Theory and Applications 1 Annalen der Physik 1 Arnold Mathematical Journal 1 Journal of Elliptic and Parabolic Equations
all top 5

Cited in 40 Fields

 228 Dynamical systems and ergodic theory (37-XX) 130 Partial differential equations (35-XX) 114 Difference and functional equations (39-XX) 76 Ordinary differential equations (34-XX) 51 Special functions (33-XX) 46 Quantum theory (81-XX) 18 Mechanics of particles and systems (70-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 15 Associative rings and algebras (16-XX) 13 Nonassociative rings and algebras (17-XX) 13 Numerical analysis (65-XX) 12 Differential geometry (53-XX) 12 Statistical mechanics, structure of matter (82-XX) 11 Algebraic geometry (14-XX) 11 Geometry (51-XX) 10 Convex and discrete geometry (52-XX) 10 Global analysis, analysis on manifolds (58-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Functions of a complex variable (30-XX) 5 Number theory (11-XX) 5 Operator theory (47-XX) 3 Commutative algebra (13-XX) 3 Functional analysis (46-XX) 3 Computer science (68-XX) 2 Field theory and polynomials (12-XX) 2 Integral transforms, operational calculus (44-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 2 Fluid mechanics (76-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX)