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Bogdanov, Leonid Vital’evich

Author ID: bogdanov.leonid-vitalevich Recent zbMATH articles by "Bogdanov, Leonid Vital’evich"
Published as: Bogdanov, L. V.
Further Spellings: Леонид Витальевич Богданов
External Links: MGP · ORCID · Google Scholar · Math-Net.Ru
Documents Indexed: 48 Publications since 1987, including 1 Book and 2 Additional arXiv Preprints
Co-Authors: 10 Co-Authors with 34 Joint Publications
299 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

35 Publications have been cited 303 times in 214 Documents Cited by Year
The non-local \({\bar \partial}\) problem and \((2+1)\)-dimensional soliton equations. Zbl 0662.35112
Bogdanov, L. V.; Manakov, S. V.
42
1988
The Boussinesq equation revisited. Zbl 0997.35068
Bogdanov, L. V.; Zakharov, V. E.
26
2002
Veselov-Novikov equation as a natural two-dimensional generalization of the Korteweg-de Vries equation. Zbl 0639.35072
Bogdanov, L. V.
26
1987
Dunajski generalization of the second heavenly equation: dressing method and the hierarchy. Zbl 1125.37047
Bogdanov, L. V.; Dryuma, V. S.; Manakov, S. V.
24
2007
Lattice and \(q\)-difference Darboux-Zakharov-Manakov systems via \(\bar \partial\)-dressing method. Zbl 0854.35111
Bogdanov, L. V.; Konopelchenko, B. G.
22
1995
Analytic-bilinear approach to integrable hierarchies. II: Multicomponent KP and 2D Toda lattice hierarchies. Zbl 0927.37053
Bogdanov, L. V.; Konopelchenko, B. G.
17
1998
Grassmannians Gr\((N - 1, N + 1)\), closed differential \((N - 1)\)-forms and \(N\)-dimensional integrable systems. Zbl 1271.37040
Bogdanov, L. V.; Konopelchenko, B. G.
13
2013
Linearly degenerate hierarchies of quasiclassical SDYM type. Zbl 1377.37093
Bogdanov, L. V.; Pavlov, M. V.
13
2017
Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type. Zbl 1209.37075
Bogdanov, L. V.; Konopelchenko, B. G.
12
2004
On dispersionless BKP hierarchy and its reductions. Zbl 1362.37123
Bogdanov, L. V.; Konopelchenko, B. G.
12
2005
On the \(\overline{\delta}\)-dressing method applicable to heavenly equation. Zbl 1345.37067
Bogdanov, L. V.; Konopelchenko, B. G.
11
2005
A class of multidimensional integrable hierarchies and their reductions. Zbl 1177.37064
Bogdanov, L. V.
10
2009
Analytic-bilinear approach to integrable hierarchies. I: Generalized KP hierarchy. Zbl 0927.37052
Bogdanov, L. V.; Konopelchenko, B. G.
8
1998
On the heavenly equation hierarchy and its reductions. Zbl 1099.37049
Bogdanov, L. V.; Konopelchenko, B. G.
8
2006
Generalized integrable hierarchies and Combescure symmetry transformations. Zbl 1001.37501
Bogdanov, L. V.; Konopelchenko, B. G.
7
1997
Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy. Zbl 1208.37040
Bogdanov, L. V.
7
2010
Doubrov-Ferapontov general heavenly equation and the hyper-Kähler hierarchy. Zbl 1346.83010
Bogdanov, L. V.
7
2015
Analytic-bilinear approach to integrable hierarchies. Zbl 0942.37048
Bogdanov, L. V.
4
1999
Generalized KP hierarchy: Möbius symmetry, symmetry constraints and Calogero-Moser system. Zbl 0988.37085
Bogdanov, L. V.; Konopelchenko, B. G.
4
2001
Nonlinear Beltrami equation and \(\tau \)-function for dispersionless hierarchies. Zbl 1118.81314
Bogdanov, L. V.; Konopelchenko, B. G.
4
2004
Semiclassical \(\overline\partial \)-method: generating equations for dispersionless integrable hierarchies. Zbl 1068.37048
Bogdanov, L. V.; Konopelchenko, B. G.; Martínez Alonso, L.
3
2003
On a class of reductions of the Manakov-Santini hierarchy connected with the interpolating system. Zbl 1186.37073
Bogdanov, L. V.
3
2010
SDYM equations on the self-dual background. Zbl 1390.81304
Bogdanov, L. V.
3
2017
A nonlocal Hamiltonian formalism for semi-Hamiltonian systems of the hydrodynamic type. Zbl 0965.37045
Bogdanov, L. V.; Ferapontov, E. V.
2
1998
Projective differential geometry of higher reductions of the two-dimensional Dirac equation. Zbl 1087.53017
Bogdanov, L. V.; Ferapontov, E. V.
2
2004
Decreasing solutions and dispersion laws in the \((2n+1)\)-dimensional dressing method. Zbl 0791.35110
Bogdanov, L. V.; Zakharov, V. E.
2
1991
Generalized Hirota bilinear identity and integrable \(q\)-difference and lattice hierarchies. Zbl 1194.39013
Bogdanov, L. V.
2
1995
Matrix extension of the Manakov-Santini system and an integrable chiral model on an Einstein-Weyl background. Zbl 1445.37046
Bogdanov, L. V.
2
2019
Generic solutions for some integrable lattice equations. Zbl 0850.35095
Bogdanov, L. V.
1
1994
Decreasing solutions and dispersion laws in the \((2n+1)\)-dimensional covering method. Zbl 0751.35038
Bogdanov, L. V.; Zakharov, V. E.
1
1991
On some developments of the \(\overline \partial\)-dressing method. Zbl 0813.35102
Bogdanov, L. V.; Zakharov, V. E.
1
1994
On the two-dimensional Zakharov-Shabat problem. Zbl 0639.35067
Bogdanov, L. V.
1
1987
Six-dimensional heavenly equation. Dressing scheme and the hierarchy. Zbl 1404.37079
Bogdanov, L. V.; Pavlov, M. V.
1
2019
Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background. Zbl 1453.81047
Bogdanov, L. V.
1
2020
Integrable \((1+1)\)-dimensional systems and the Riemann problem with a shift. Zbl 0811.35094
Bogdanov, L. V.; Zakharov, V. E.
1
1994
Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background. Zbl 1453.81047
Bogdanov, L. V.
1
2020
Matrix extension of the Manakov-Santini system and an integrable chiral model on an Einstein-Weyl background. Zbl 1445.37046
Bogdanov, L. V.
2
2019
Six-dimensional heavenly equation. Dressing scheme and the hierarchy. Zbl 1404.37079
Bogdanov, L. V.; Pavlov, M. V.
1
2019
Linearly degenerate hierarchies of quasiclassical SDYM type. Zbl 1377.37093
Bogdanov, L. V.; Pavlov, M. V.
13
2017
SDYM equations on the self-dual background. Zbl 1390.81304
Bogdanov, L. V.
3
2017
Doubrov-Ferapontov general heavenly equation and the hyper-Kähler hierarchy. Zbl 1346.83010
Bogdanov, L. V.
7
2015
Grassmannians Gr\((N - 1, N + 1)\), closed differential \((N - 1)\)-forms and \(N\)-dimensional integrable systems. Zbl 1271.37040
Bogdanov, L. V.; Konopelchenko, B. G.
13
2013
Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy. Zbl 1208.37040
Bogdanov, L. V.
7
2010
On a class of reductions of the Manakov-Santini hierarchy connected with the interpolating system. Zbl 1186.37073
Bogdanov, L. V.
3
2010
A class of multidimensional integrable hierarchies and their reductions. Zbl 1177.37064
Bogdanov, L. V.
10
2009
Dunajski generalization of the second heavenly equation: dressing method and the hierarchy. Zbl 1125.37047
Bogdanov, L. V.; Dryuma, V. S.; Manakov, S. V.
24
2007
On the heavenly equation hierarchy and its reductions. Zbl 1099.37049
Bogdanov, L. V.; Konopelchenko, B. G.
8
2006
On dispersionless BKP hierarchy and its reductions. Zbl 1362.37123
Bogdanov, L. V.; Konopelchenko, B. G.
12
2005
On the \(\overline{\delta}\)-dressing method applicable to heavenly equation. Zbl 1345.37067
Bogdanov, L. V.; Konopelchenko, B. G.
11
2005
Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type. Zbl 1209.37075
Bogdanov, L. V.; Konopelchenko, B. G.
12
2004
Nonlinear Beltrami equation and \(\tau \)-function for dispersionless hierarchies. Zbl 1118.81314
Bogdanov, L. V.; Konopelchenko, B. G.
4
2004
Projective differential geometry of higher reductions of the two-dimensional Dirac equation. Zbl 1087.53017
Bogdanov, L. V.; Ferapontov, E. V.
2
2004
Semiclassical \(\overline\partial \)-method: generating equations for dispersionless integrable hierarchies. Zbl 1068.37048
Bogdanov, L. V.; Konopelchenko, B. G.; Martínez Alonso, L.
3
2003
The Boussinesq equation revisited. Zbl 0997.35068
Bogdanov, L. V.; Zakharov, V. E.
26
2002
Generalized KP hierarchy: Möbius symmetry, symmetry constraints and Calogero-Moser system. Zbl 0988.37085
Bogdanov, L. V.; Konopelchenko, B. G.
4
2001
Analytic-bilinear approach to integrable hierarchies. Zbl 0942.37048
Bogdanov, L. V.
4
1999
Analytic-bilinear approach to integrable hierarchies. II: Multicomponent KP and 2D Toda lattice hierarchies. Zbl 0927.37053
Bogdanov, L. V.; Konopelchenko, B. G.
17
1998
Analytic-bilinear approach to integrable hierarchies. I: Generalized KP hierarchy. Zbl 0927.37052
Bogdanov, L. V.; Konopelchenko, B. G.
8
1998
A nonlocal Hamiltonian formalism for semi-Hamiltonian systems of the hydrodynamic type. Zbl 0965.37045
Bogdanov, L. V.; Ferapontov, E. V.
2
1998
Generalized integrable hierarchies and Combescure symmetry transformations. Zbl 1001.37501
Bogdanov, L. V.; Konopelchenko, B. G.
7
1997
Lattice and \(q\)-difference Darboux-Zakharov-Manakov systems via \(\bar \partial\)-dressing method. Zbl 0854.35111
Bogdanov, L. V.; Konopelchenko, B. G.
22
1995
Generalized Hirota bilinear identity and integrable \(q\)-difference and lattice hierarchies. Zbl 1194.39013
Bogdanov, L. V.
2
1995
Generic solutions for some integrable lattice equations. Zbl 0850.35095
Bogdanov, L. V.
1
1994
On some developments of the \(\overline \partial\)-dressing method. Zbl 0813.35102
Bogdanov, L. V.; Zakharov, V. E.
1
1994
Integrable \((1+1)\)-dimensional systems and the Riemann problem with a shift. Zbl 0811.35094
Bogdanov, L. V.; Zakharov, V. E.
1
1994
Decreasing solutions and dispersion laws in the \((2n+1)\)-dimensional dressing method. Zbl 0791.35110
Bogdanov, L. V.; Zakharov, V. E.
2
1991
Decreasing solutions and dispersion laws in the \((2n+1)\)-dimensional covering method. Zbl 0751.35038
Bogdanov, L. V.; Zakharov, V. E.
1
1991
The non-local \({\bar \partial}\) problem and \((2+1)\)-dimensional soliton equations. Zbl 0662.35112
Bogdanov, L. V.; Manakov, S. V.
42
1988
Veselov-Novikov equation as a natural two-dimensional generalization of the Korteweg-de Vries equation. Zbl 0639.35072
Bogdanov, L. V.
26
1987
On the two-dimensional Zakharov-Shabat problem. Zbl 0639.35067
Bogdanov, L. V.
1
1987
all top 5

Cited by 213 Authors

17 Ferapontov, Evgeny Vladimirovich
14 Konopelchenko, Boris Georgievich
13 Bogdanov, Leonid Vital’evich
10 Doliwa, Adam
10 Pavlov, Maxim V.
10 Pogrebkov, Andrei K.
9 Zenchuk, Alexandre I.
8 Dubrovsky, V. G.
8 Prykarpatsky, Anatoliy Karolevych
8 Zhu, Junyi
7 Morozov, Oleg I.
7 Prykarpatsky, Yarema Anatoliyovych
7 Schief, Wolfgang Karl
6 Khabibullin, Ismagil Talgatovich
5 Dunajski, Maciej
5 Kruglikov, Boris S.
5 Novikov, Vladimir S.
4 Blackmore, Denis L.
4 Fan, Engui
4 Hentosh, Oksana E.
4 Luo, Jinghua
4 Santini, Paolo Maria
4 Sergeev, Sergeĭ Mikhaĭlovich
4 Taĭmanov, Iskander Asanovich
4 Topovsky, A. V.
4 Wang, Xueru
3
3 Bridges, Thomas J.
3 Chang, Jen-Hsu
3 Chen, Yu-Tung
3 Grinevich, Pëtr Georgievich
3 Kulaev, Ruslan Chermenovich
3 Shabat, Alekseĭ Borisovich
3 Szereszewski, Adam
3 Tian, Shoufu
2 Berjawi, S.
2 Błaszak, Maciej
2 Bobenko, Alexander Ivanovich
2 Boiti, Marco
2 Cheng, Jia
2 Chesnokov, Alexander A.
2 Dimakis, Aristophanes
2 Doubrov, Boris M.
2 Khakimova, Aĭgul’ Rinatovna
2 Khusnutdinova, Karima Robertovna
2 Korotyaev, Evgeny L.
2 Kuang, Yonghui
2 Lelito, Aleksandra
2 Li, Biao
2 Lin, Runliang
2 Mañas, Manuel
2 Müller-Hoissen, Folkert
2 Nijhoff, Frank W.
2 Pempinelli, Flora
2 Poptsova, Mariya Nikolaevna
2 Qiao, Zhijun
2 Ratliff, Daniel J.
2 Rogers, Colin
2 Stoilov, Nikola M.
2 Suris, Yuri Borisovich
2 Szablikowski, Błażej M.
2 Takebe, Takashi
2 Tsarev, Sergej Petrovich
2 Tu, Minghsien
2 Xue, Lingling
2 Zakharov, Vladimir Evgen’evich
1 Adler, Vsevolod Eduardovich
1 Affolter, Niklas Christoph
1 Akhmedova, Valeria
1 Anco, Stephen C.
1 Angelopoulos, Yannis
1 Ariznabarreta, Gerardo
1 Artemovych, Orest Dem”yanovych
1 Athorne, Chris
1 Atiyah, Michael Francis
1 Badanin, Andrey
1 Bai, Yang
1 Bakholdin, Igor B.
1 Basalaev, M. Yu.
1 Başar, Gökçe
1 Bazhanov, Vladimir V.
1 Bhat, Vishesh S.
1 Bulchandani, Vir B.
1 Burovskiy, P. A.
1 Cieśliński, Jan L.
1 Corrigan, Edward
1 Danlybaeva, A. K.
1 de Tilière, Béatrice
1 Dunne, Gerald V.
1 Eilbeck, John Chris
1 El, Gennady A.
1 Engelbrecht, Jüri
1 Enolskiĭ, Viktor Zelikovich
1 Ferguson, James T.
1 Folguera, Alejandra
1 Gandarias Núñez, Maria Luz
1 Gao, Yitian
1 García-Ardila, Juan Carlos
1 Gavrilyuk, Sergey L.
1 Geng, Xianguo
...and 113 more Authors
all top 5

Cited in 64 Serials

29 Journal of Mathematical Physics
25 Theoretical and Mathematical Physics
21 Journal of Geometry and Physics
11 Journal of Physics A: Mathematical and Theoretical
9 Physica D
8 Journal of Nonlinear Mathematical Physics
6 Communications in Mathematical Physics
6 Studies in Applied Mathematics
6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
5 Applied Mathematics Letters
5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
4 Letters in Mathematical Physics
4 Journal of Differential Equations
3 Journal of Mathematical Analysis and Applications
3 Ukrainian Mathematical Journal
3 Acta Applicandae Mathematicae
3 Journal of Mathematical Sciences (New York)
2 Classical and Quantum Gravity
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Physics Letters. A
2 Reports on Mathematical Physics
2 Wave Motion
2 Applied Mathematics and Computation
2 Differential Geometry and its Applications
2 SIAM Journal on Applied Mathematics
2 Russian Mathematics
2 Mathematical Physics, Analysis and Geometry
2 Communications in Nonlinear Science and Numerical Simulation
2 Advances in Mathematical Physics
2 Ufimskiĭ Matematicheskiĭ Zhurnal
2 Symmetry
2 Analysis and Mathematical Physics
1 Indian Journal of Pure & Applied Mathematics
1 Mathematical Notes
1 Nonlinearity
1 Physics Letters. B
1 Geometriae Dedicata
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Approximation Theory
1 Mathematics and Computers in Simulation
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Tôhoku Mathematical Journal. Second Series
1 International Journal of Mathematics
1 Computational Mathematics and Mathematical Physics
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Experimental Mathematics
1 St. Petersburg Mathematical Journal
1 Opuscula Mathematica
1 Doklady Mathematics
1 Journal of Applied Mechanics and Technical Physics
1 Acta Mathematica Sinica. English Series
1 Journal of High Energy Physics
1 Annales Henri Poincaré
1 Qualitative Theory of Dynamical Systems
1 Czechoslovak Journal of Physics
1 JP Journal of Geometry and Topology
1 Communications on Pure and Applied Analysis
1 Journal of Statistical Mechanics: Theory and Experiment
1 Proceedings of the Steklov Institute of Mathematics
1 Journal of Biological Dynamics
1 Communications in Theoretical Physics
1 Mathematics
1 European Journal of Mathematics
1 Combinatorial Theory

Citations by Year