Russian Academy of Sciences

Landau Institute for Theoretical Physics

Leonid V. Bogdanov

Senior researcher

Doctor of science

Work phone: (+7 495) 702-93-17
Email:
Homepage: http://itp.ac.ru/~leonid/

Publications

    1. L.V. Bogdanov, O nekotorykh lineinykh uravneniyakh, svyazannykh s bezdispersionnymi integriruemymi sistemami, Teoreticheskaya i matematicheskaya fizika, 221(1), 3-17 (2024) [L.V. Bogdanov, On some linear equations associated with dispersionless integrable systems, Theoret. and Math. Phys., 221(1), 1589-1602 (2024)]; arXiv:2404.18078, ADS: 2024arXiv240418078B, RINTs: 74172830, zbMath: arXiv:2404.18078, EDN: QPTZML.
    2. L.V. Bogdanov, Lin-Lin Syue, Klass reduktsii dvukhkomponentnoi ierarkhii Kadomtseva–Petviashvili i sistema Khiroty–Okhty, TMF, 211(1), 37-47 (2022) [L.V. Bogdanov, Lingling Xue, A class of reductions of the two-component KP hierarchy and the Hirota-Ohta system, Theor. Math. Phys., 211(1), 473-482 (2022)]; arXiv:2112.12759, Scopus: 2-s2.0-85128903245, ADS: 2022TMP...211..473B, RINTs: 48514139, MathSciNet: 4461512, zbMath: 1515.37067, EDN: NJODQW.
    3. L.V. Bogdanov, Dispersionless BKP equation, the Manakov-Santini system and Einstein-Weyl structures, Symmetry, 13(9), 1699 (2021); arXiv:2108.03078, WoS: 000701168700001, Scopus: 2-s2.0-85115133015, ADS: 2021Symm...13.1699B, InSpire: 1900991, RINTs: 47090710, zbMath: 1453.81047.
    4. L.V. Bogdanov, Matrichnoe rasshirenie mnogomernykh bezdispersionnykh integriruemykh ierarkhii, TMF, 209(1), 3-15 (2021) [L.V. Bogdanov, Matrix extension of multidimensional dispersionless integrable hierarchies, Theoret. Math. Phys., 209(1), 1319-1330 (2021)]; arXiv:2105.14264, WoS: 000708924700001, Scopus: 2-s2.0-85117417985, ADS: 2021TMP...209.1319B, InSpire: 1866111, RINTs: 46664897, MathSciNet: 4324110, zbMath: 1515.37066, EDN: WTYZUI.
    5. L.V. Bogdanov, Bezdispersionnye integriruemye sistemy i uravneniya Bogomol’nogo na fone geometrii Einshteina–Veilya, TMF, 205(1), 41-54 (2020) [L.V. Bogdanov, Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background, Theor. Math. Phys., 205(1), 1279-1290 (2020)]; arXiv:2005.09906, WoS: 000584562700003, Scopus: 2-s2.0-85093842063, ADS: 2020TMP...205.1279B, InSpire: 1797076, RINTs: 46681694, MathSciNet: 4156833, zbMath: 1453.81047.
    6. L.V. Bogdanov, B.G. Konopelchenko, Integrability properties of a symmetric 4 + 4-dimensional heavenly-type equation, J. Phys. A 52, 355204 (2019); arXiv:1905.00887, WoS: 000478955100002, Scopus: 2-s2.0-85072403976, ADS: 2019JPhA...52I5204B, RINTs: 38617461, MathSciNet: 4002496, zbMath: 1509.37082.
    7. L.V. Bogdanov, M.V. Pavlov, Six-dimensional heavenly equation. Dressing scheme and the hierarchy, Physics Letters A, 383(1), 10-14 (2019); arXiv:1806.01500, WoS: 000452585900002, Scopus: 2-s2.0-85054170254, ADS: 2019PhLA..383...10B, InSpire: 1676391, RINTs: 38617461, MathSciNet: 3869742, zbMath: 1404.37079.
    8. L.V. Bogdanov, Matrichnoe rasshirenie sistemy Manakova–Santini i integriruemaya kiral’naya model’ na fone geometrii Einshteina–Veilya, TMF, 201(3), 337-346 (2019) [L.V. Bogdanov, Matrix extension of the Manakov-Santini system and integrable chiral model on Einstein-Weyl background, Theor. Math. Phys., 201(3), 1701-1709 (2019)]; arXiv:1907.01964, WoS: 000511860000003, Scopus: 2-s2.0-85077588700, ADS: 2020TMP...201.1701B, RINTs: 41562853, MathSciNet: 4036825, zbMath: 1445.37046.
    9. L.V. Bogdanov, M.V. Pavlov, Linearly degenerate hierarchies of quasiclassical SDYM type, J. Math. Phys. 58, 093505 (2017); arXiv:1603.00238, WoS: 000412102600031, Scopus: 2-s2.0-85030148520, ADS: 2017JMP....58i3505B, RINTs: 31062499, MathSciNet: 3705665, zbMath: 1377.37093.
    10. L.V. Bogdanov, SDYM equations on the self-dual background, J. Phys. A 50, 19LT02 (2017); arXiv:1612.04536, WoS: 000399406600001, Scopus: 2-s2.0-85018500082, ADS: 2017JPhA...50sLT02B, InSpire: 1503388, RINTs: 41776681, MathSciNet: 3639710, zbMath: 1390.81304.
    11. L.V. Bogdanov, Doubrov-Ferapontov general heavenly equation and the hyper-Kähler hierarchy, J. Phys. A: Math. Theor. 48, 235202 (2015); arXiv:1412.7376, WoS: 000355211700006, Scopus: 2-s2.0-84930003827, ADS: 2015JPhA...48w5202B, InSpire: 1335402, RINTs: 24034952, MathSciNet: 3355233, zbMath: 1346.83010.
    12. L.V. Bogdanov, B.G. Konopelchenko, Projective differential geometry of multidimensional dispersionless integrable hierarchies, J. Phys. Conf. Ser., 482, 012005 (2014); arXiv:1310.0203, WoS: 000334352400005, Scopus: 2-s2.0-84896934060, ADS: 2014JPhCS.482a2005B, InSpire: 1256306, RINTs: 21869033, MathSciNet: -, zbMath: arXiv:1310.0203.
    13. L.V. Bogdanov, B.G. Konopelchenko, Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems, J. Phys. A 46, 085201 (2013); arXiv:1208.6129, WoS: 000314821900004, Scopus: 2-s2.0-84874150309, ADS: 2013JPhA...46h5201B, RINTs: 20435346, MathSciNet: 3030187, zbMath: 1271.37040.
    14. L.V. Bogdanov, Dunajski–Tod equation and reductions of the generalized dispersionless 2DTL hierarchy, Phys. Lett. A 376(45), 2894–2898 (2012); arXiv:1204.3780, WoS: 000311865500015, Scopus: 2-s2.0-84868135150, ADS: 2012PhLA..376.2894B, InSpire: 1111136, RINTs: 20498135, MathSciNet: 2997171, zbMath: -.
    15. L.V. Bogdanov, Interpoliruyushchie differentsial’nye reduktsii mnogomernykh integriruemykh ierarkhii, TMF, 167(3), 354–363 (2011) [L.V. Bogdanov, Interpolating differential reductions of multidimensional integrable hierarchies, Theor. Math. Phys., 167(3), 705-713 (2011)]; arXiv:1011.0631, WoS: 000293653700003, Scopus: 2-s2.0-79960087346, ADS: 2011TMP...167..705B, RINTs: 20732307, MathSciNet: 3166377, zbMath: -.
    16. L.V. Bogdanov, On a class of reductions of the Manakov-Santini hierarchy connected with the interpolating system, J. Phys. A: Math. Theor. 43, 115206 (2010) (11pp); arXiv:0910.4004, WoS: 000275121400008, Scopus: 2-s2.0-77649257606, ADS: 2010JPhA...43k5206B, RINTs: 15331793, MathSciNet: 2595271, zbMath: 1186.37073.
    17. L.V. Bogdanov, Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy, J. Phys. A: Math. Theor. 43, 434008 (2010); arXiv:1003.0287, WoS: 000283300100009, Scopus: 2-s2.0-78649644928, ADS: 2010JPhA...43Q4008B, RINTs: 16919470, MathSciNet: 2727782, zbMath: 1208.37040.
    18. L.V. Bogdanov, O klasse mnogomernykh integriruemykh ierarkhii i ikh reduktsiyakh, TMF, 160(1), 15-22 (2009) [L.V. Bogdanov, A class of multidimensional integrable hierarchies and their reductions, Theor. Math. Phys., 160(1), 887-893 (2009)]; arXiv:0810.2397, WoS: 000269118900002, Scopus: -, ADS: 2009TMP...160..887B, RINTs: 20732046, MathSciNet: 2603894, zbMath: 1177.37064.
    19. L.V. Bogdanov, Jen-H. Chang, Yu-T. Chen, Generalized dKP: Manakov-Santini hierarchy and its waterbag reduction, arXiv:0810.0556, ADS: 2008arXiv0810.0556B.
    20. V. Dryuma, L. Bogdanov, On nonlinear equations connected with six-dimensional Plebanski space, arXiv:0812.1637, ADS: 2008arXiv0812.1637D.
    21. L.V. Bogdanov, V.S. Dryuma, S.V. Manakov, Dunajski generalization of the second heavenly equation: dressing method and the hierarchy, J. Phys. A 40(48), 14383-14393 (2007); arXiv:0707.1675, WoS: 000251786700006, Scopus: 2-s2.0-36248992862, ADS: 2007JPhA...4014383B, RINTs: 13538690, MathSciNet: 2431852, zbMath: 1125.37047.
    22. L.V. Bogdanov, B.G. Konopelchenko, On the heavenly equation hierarchy and its reductions, J. Phys. A 39(38), 11793-11802 (2006); nlin/0512074, WoS: 000241555600007, Scopus: 2-s2.0-33748548671, ADS: 2006JPhA...3911793B, InSpire: 702178, RINTs: 13517547, MathSciNet: 2275882, zbMath: 1099.37049.
    23. L.V. Bogdanov, V.S. Dryuma, S.V. Manakov, On the dressing method for Dunajski anti-self-duality equation, nlin/0612046, ADS: 2006nlin.....12046B.
    24. L.V. Bogdanov, B.G. Konopelchenko, On dispersionless BKP hierarchy and its reductions, J. Nonlinear Math. Phys., 12, Suppl.1, 64-73 (2005); nlin/0411046, WoS: 000226501000008, Scopus: 2-s2.0-30444450575, ADS: 2005JNMP...12S..64B, RINTs: 13488253, MathSciNet: 2117170, zbMath: 1362.37123.
    25. L.V. Bogdanov, B.G. Konopelchenko, On the δ¯-dressing method applicable to heavenly equation, Phys. Lett. A 345(1-3), 137-143 (2005); nlin/0504062, WoS: 000232070300016, Scopus: 2-s2.0-24644455485, ADS: 2005PhLA..345..137B, InSpire: 702177, RINTs: 13487743, MathSciNet: 2169964, zbMath: 1345.37067.
    26. L.V. Bogdanov, E.V. Ferapontov, Projective differential geometry of higher reductions of the two-dimensional Dirac equation, J. Geom. Phys., 52(3), 328-352 (2004); nlin/0211040, WoS: 000225119200007, Scopus: 2-s2.0-7044237488, ADS: 2004JGP....52..328B, RINTs: 13461756, MathSciNet: 2099157, zbMath: 1087.53017.
    27. L.V. Bogdanov, B.G. Konopelchenko, Nonlinear Beltrami equation and τ-function for dispersionless hierarchies, Phys. Lett. A 322(5-6), 330-337 (2004); nlin/0310038, WoS: 000220123600011, Scopus: 2-s2.0-1442277655, ADS: 2004PhLA..322..330B, RINTs: 13453262, MathSciNet: 2049042, zbMath: 1118.81314.
    28. L.V. Bogdanov, B.G. Konopelchenko, Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type, Phys. Lett. A 330(6), 448-459 (2004); nlin/0312013, WoS: 000224161400008, Scopus: 2-s2.0-5444265956, ADS: 2004PhLA..330..448B, RINTs: 13447795, MathSciNet: 2094456, zbMath: 1209.37075.
    29. L.V. Bogdanov, B.G. Konopel’chenko, A. Moro, Simmetriinye reduktsii veshchestvennogo bezdispersnogo uravneniya Veselova-Novikova., Fundament. i prikl. matem., 10(1), 5-15 (2004) [L.V. Bogdanov, B.G. Konopelchenko, A. Moro, Symmetry constraints for real dispersionless Veselov-Novikov equation, J. Math. Sci., 136(6), 4411-4418 (2006)]; nlin/0406023, WoS: -, Scopus: 2-s2.0-33745636609, ADS: 2004nlin......6023B, RINTs: 9068290, MathSciNet: 2119748, zbMath: 1073.35034.
    30. L.V. Bogdanov, B.G. Konopel’chenko, L.M. Alonso, Kvaziklassicheskii ∂¯-metod: proizvodyashchie uravneniya dlya bezdispersionnykh integriruemykh ierarkhii, TMF, 134(1), 46-54 (2003) [L.V. Bogdanov, B.G. Konopelchenko, L.M. Alonso, Semiclassical ∂¯-method: Generating equations for dispersionless integrable hierarchies, Theor. Math. Phys., 134 (1), 39-46 (2003)]; nlin/0111062, WoS: 000181042100004, Scopus: 2-s2.0-0347125041, ADS: 2001nlin.....11062B, RINTs: 13440465, MathSciNet: 2021729, zbMath: 1068.37048.
    31. L.V. Bogdanov, V.E. Zakharov, The Boussinesq equation revisited, Physica D 165 (3-4), 137-162 (2002), WoS: 000176132500002, Scopus: 2-s2.0-0037092882, ADS: 2002PhyD..165..137B, RINTs: 13405665, MathSciNet: 1910292, zbMath: 0997.35068, EDN: LHJGQZ.
    32. L.V. Bogdanov, B.G. Konopelchenko, Generalized KP hierarchy: Möbius symmetry, symmetry constraints and Calogero–Moser system, Physica D 152-153, 85-96 (2001); solv-int/9912005, WoS: 000168986300010, Scopus: 2-s2.0-0035873626, ADS: 2001PhyD..152...85B, RINTs: 13374767, MathSciNet: 1837900, zbMath: 0988.37085.
    33. L.V. Bogdanov, B.G. Konopelchenko, A.Yu. Orlov, Trigonometric Calogero-Moser System as a Symmetry Reduction of KP Hierarchy, NATO Science Series II: Math. Phys. Chem., Vol. 18, 277-287 (2001) [Integrable Hierarchies and Modern Physical Theories: Proc. NATO Adv. Research Workshop, Chicago, USA, July 22-26, 2000. Ed. by H. Aratyn, A.S. Sorin, Kluwer Academic Publishers, 2001, 448 pp., ISBN 978-0-7923-6963]; nlin/0011007, ADS: 2000nlin.....11007B, MathSciNet: 1896855, zbMath: 0980.37023.
    34. L.V. Bogdanov, B.G. Konopelchenko, Möbius invariant integrable lattice equations associated with the generalized KP hierarchy, CRM Proc. Lect. Notes, 25, 33-45 (2000) [SIDE III – Symmetries and Integrability of Difference Equations: Proc. 3rd Conf., Sabaudia, Italy, May 16-22, 1998. Ed. by D. Levi at al., AMS, 2000. xvi+444 pp. ISBN 0-8218-2128-8], MathSciNet: 1771707, zbMath: 0958.37059.
    35. L.V. Bogdanov, B.G. Konopelchenko, Möbius symmetry, KP symmetry constraints and Calogero-Moser system, Proc. Workshop on Nonlinearity, Integrability and all That: Twenty years after NEEDS'79, Lecce, Italy, July 1-10, 1999. Ed. by M. Boiti et al., World Scientific, p. 237-243 (2000), MathSciNet: 1772984, zbMath: 0966.35110.
    36. L.V. Bogdanov, B.G. Konopelchenko, Möbius invariant integrable lattice equations associated with KP and 2DTL hierarchies, Phys. Lett. A 256 (1), 39-46 (1999); solv-int/9806008, WoS: 000080681300007, Scopus: 2-s2.0-0010232459, ADS: 1999PhLA..256...39B, InSpire: -, RINTs: 13320346, MathSciNet: 1691502, zbMath: 0935.37030.
    37. L.V. Bogdanov, Analytic-bilinear approach to integrable hierarchies, Dordrecht: Kluwer Academic Publishers. 1999, xii, 264 pp. ISBN 0-7923-5919-4 [Mathematics and its Applications (Dordrecht), 493], zbMath: 0942.37048.
    38. L.V. Bogdanov, B.G. Konopelchenko, Analytic-bilinear approach to integrable hierarchies. I. Generalized KP hierarchy, J. Math. Phys., 39 (9), 4683-4700 (1998); solv-int/9609009, WoS: 000075617100024, Scopus: 2-s2.0-0032345403, ADS: 1996solv.int..9009B, RINTs: 13290617, MathSciNet: 1643321, zbMath: 0927.37052.
    39. L.V. Bogdanov, B.G. Konopelchenko, Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies, J. Math. Phys., 39 (9), 4701-4728 (1998); solv-int/9705009, WoS: 000075617100025, Scopus: 2-s2.0-0032346407, ADS: 1998JMP....39.4701B, RINTs: 13298851, MathSciNet: 1643325, zbMath: 0927.37053.
    40. L.V. Bogdanov, E.V. Ferapontov, Nelokal’nyi gamil’tonov formalizm polugamil’tonovykh sistem gidrodinamicheskogo tipa, TMF, 116(1), 113-121 (1998) [L.V. Bogdanov, E.V. Ferapontov, A nonlocal Hamiltonian formalism for semi-Hamiltonian systems of the hydrodynamic type, Theor. Math. Phys., 116(1), 829-835 (1998)], WoS: 000076425700004, Scopus: 2-s2.0-0040583701, ADS: 1998TMP...116..829B, RINTs: 13291006, MathSciNet: 1700693, zbMath: 0965.37045.
    41. L.V. Bogdanov, B.G. Konopelchenko, Generalized integrable hierarchies and Combescure symmetry transformations, J. Phys. A 30 (5), 1591-1603 (1997); solv-int/9606007, WoS: A1997WN36600022, Scopus: 2-s2.0-0031557253, ADS: 1997JPhA...30.1591B, InSpire: -, RINTs: 13254651, MathSciNet: 1449999, zbMath: 1001.37501.
    42. L.V. Bogdanov, B.G. Konopelchenko, Continuous, lattice and q-difference integrable systems and their transformation properties via ∂¯ -dressing method., Nonlinear physics: theory and experiment. Nature, structure and properties of nonlinear phenomena. Proceedings of the workshop, Lecce, Italy, June 29-July 7, 1995. Ed. by E. Alfinito et al., Singapore: World Scientific. 29-36 (1996), zbMath: 0941.37551.
    43. L.V. Bogdanov, B.G. Konopelchenko, Lattice and q-difference Darboux-Zakharov-Manakov systems via ∂¯-dressing method, J. Phys. A 28 (5), L173-L178 (1995); solv-int/9501007, WoS: A1995QL48500005, Scopus: 2-s2.0-35748954153, ADS: 1995JPhA...28L.173B, RINTs: 31381130, MathSciNet: -, zbMath: 0854.35111.
    44. L.V. Bogdanov, Generalized Hirota bilinear identity and integrable q-difference and lattice hierarchies, Physica D 87 (1-4), 58-63 (1995); q-alg/9501031, WoS: A1995TB22600010, Scopus: 2-s2.0-0041049000, ADS: 1995PhyD...87...58B, MathSciNet: 1361668, zbMath: 1194.39013.
    45. L.V. Bogdanov, V.E. Zakharov, Integrable (1+1)-dimensional systems and the Riemann problem with a shift, Inverse Problems, 10(4), 817-835 (1994), WoS: A1994PB74500004, Scopus: 2-s2.0-0006065293, ADS: 1994InvPr..10..817B, MathSciNet: 1286623, zbMath: 0811.35094.
    46. L.V. Bogdanov, V.E. Zakharov, On some developments of the ∂¯-dressing method, Algebra i analiz, 6(3), 40-58 (1994); ispravlenie - tam zhe, 7(1),224 (1995) [St. Petersburg Math. J., 6(3), 475-493 (1995)], MathSciNet: 1301829, zbMath: 0813.35102.
    47. L.V. Bogdanov, Generic solutions for some integrable lattice equations, TMF, 99(2), 177-184 (1994) [Theor. Math. Phys., 99(2), 505-510 (1994)]; hep-th/9401080, WoS: A1994PV07100003, Scopus: 2-s2.0-34249765238, ADS: 1994TMP....99..505B, InSpire: 37045, MathSciNet: 1308778, zbMath: 0850.35095.
    48. L.V. Bogdanov, V.E. Zakharov, Ubyvayushchie resheniya i zakony dispersii v (2+1)-mernom metode odevaniya, Algebra i analiz, 3 (3), 49-56 (1991) [L.V. Bogdanov, V.E. Zakharov, Decreasing solutions and dispersion laws in the (2n+1)-dimensional covering method, St. Petersburg Math. J., 3(3), 533-540 (1992)], MathSciNet: 1150552, zbMath: 0751.35038.
    49. L.V. Bogdanov, S.V. Manakov, The non-local ∂¯ problem and (2+1)-dimensional soliton equations, J. Phys. A 21(10), L537-L544 (1988), WoS: A1988T047900001, Scopus: 2-s2.0-0001196550, MathSciNet: 0953203, zbMath: 0662.35112.
    50. L.V. Bogdanov, S.V. Manakov, Nonlocal ∂¯-problem and (2+1) -dimensional soliton equations, In: Plasma theory and nonlinear and turbulent processes in physics. Proc. Int. Workshop, Kiev, USSR, 13-25 April 1987, Vol.1, 7-19 (1988). Ed. by V.G. Bar'yakhtar, V.M. Chernousenko, N.S. Erokhin, A.G. Sitenko, V.E. Zakharov. World Scientific, 1988. Vols. 1,2. xv, 998 pp. ISBN 9971-50-546-0, MathSciNet: 0957154, zbMath: 0682.35092.
    51. S.V. Manakov, L.V. Bogdanov, Nonlocal problems of complex analysis and related nonlinear equations, Physica D 28 (1-2), 222-222 (1987), WoS: A1987K345100024.
    52. L.V. Bogdanov, Uravnenie Veselova–Novikova kak estestvennoe dvumernoe obobshchenie uravneniya Kortevega–de Friza, TMF, 70(2), 309-314 (1987) [L.V. Bogdanov, Veselov-Novikov equation as a natural two-dimensional generalization of the Korteweg-de Vries equation, Theor. Math. Phys., 70(2), 219-223 (1987)], MathSciNet: 0894472, zbMath: 0639.35072.
    53. L.V. Bogdanov, O dvumernoi zadache Zakharova–Shabata, TMF, 72(1), 155-159 (1987) [L.V. Bogdanov, On the two-dimensional Zakharov-Shabat problem, Theor. Math. Phys., 72(1), 790-793 (1987)], WoS: A1987M118600015, MathSciNet: 0910489, zbMath: 0639.35067.