Russian Academy of Sciences

Landau Institute for Theoretical Physics

Leonid V. Bogdanov

Senior researcher

Doctor of science

Work phone: (+7 495) 702-93-17


    1. L.V. Bogdanov, B.G. Konopelchenko, Integrability properties of symmetric 4+4-dimensional heavenly type equation, J. Phys. A, Accepted Manuscript, online 4 July 2019; arXiv:1905.00887.
    2. 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, Scopus: 2-s2.0-85054170254.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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, Scopus: 2-s2.0-77649257606.
    11. L.V. Bogdanov, Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy, J. Phys. A: Math. Theor. 43, 434008 (2010); arXiv:1003.0287, Scopus: 2-s2.0-78649644928.
    12. 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.
    13. L.V. Bogdanov, Jen-H. Chang, Yu-T. Chen, Generalized dKP: Manakov-Santini hierarchy and its waterbag reduction, arXiv:0810.0556.
    14. V. Dryuma, L. Bogdanov, On nonlinear equations connected with six-dimensional Plebanski space, arXiv:0812.1637.
    15. 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.
    16. L.V. Bogdanov, B.G. Konopelchenko, On the heavenly equation hierarchy and its reductions, J. Phys. A 39(38), 11793-11802 (2006); nlin/0512074.
    17. L.V. Bogdanov, V.S. Dryuma, S.V. Manakov, On the dressing method for Dunajski anti-self-duality equation, nlin/0612046.
    18. 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.
    19. L.V. Bogdanov, B.G. Konopelchenko, On the partial derivative-dressing method applicable to heavenly equation, Phys. Lett. A 345(1-3), 137-143 (2005); nlin/0504062.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. L.V. Bogdanov, B.G. Konopel’chenko, L.M. Alonso, Kvaziklassicheskii $\bar\partial$-metod: proizvodyashchie uravneniya dlya bezdispersionnykh integriruemykh ierarkhii, TMF, 134(1), 46-54 (2003) [L.V. Bogdanov, B.G. Konopelchenko, L.M. Alonso, Semiclassical $\dbar$-method: Generating equations for dispersionless integrable hierarchies, Theor. Math. Phys., 134 (1), 39-46 (2003)]; nlin/0111062.
    25. L.V. Bogdanov, V.E. Zakharov, The Boussinesq equation revisited, Physica D 165 (3-4), 137-162 (2002).
    26. 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.
    27. 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.
    28. 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. ISBN 0-8218-2128-8].
    29. 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).
    30. 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.
    31. 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].
    32. 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.
    33. 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.
    34. 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)].
    35. L.V. Bogdanov, B.G. Konopelchenko, Generalized integrable hierarchies and Combescure symmetry transformations, J. Phys. A 30 (5), 1591-1603 (1997); solv-int/9606007.
    36. L.V. Bogdanov, B.G. Konopelchenko, Continuous, lattice and $q$-difference integrable systems and their transformation properties via $\overline \partial$-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).
    37. L.V. Bogdanov, B.G. Konopelchenko, Lattice and q-difference Darboux-Zakharov-Manakov systems via $\dbar$-dressing method, J. Phys. A 28 (5), L173-L178 (1995); solv-int/9501007.
    38. 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.
    39. 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).
    40. L.V. Bogdanov, V.E. Zakharov, On some developments of the $\dbar$-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)].
    41. 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.
    42. 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)].
    43. L.V. Bogdanov, S.V. Manakov, The non-local $\dbar$ problem and (2+1)-dimensional soliton equations, J. Phys. A 21(10), L537-L544 (1988).
    44. L.V. Bogdanov, S.V. Manakov, Nonlocal ${\bar \partial}$-problem and $(2+1)$-dimensional soliton equations, Plasma theory and nonlinear and turbulent processes in physics. Proc. Int. Workshop, Kiev, USSR, 13-25 April 1987, 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.
    45. S.V. Manakov, L.V. Bogdanov, Nonlocal problems of complex analysis and related nonlinear equations, Physica D 28 (1-2), 222-222 (1987).
    46. 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)].
    47. 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)].