Research area:

The theory of nonlinear phenomena in condensed matter physics based on the soliton concept and its applications for description of nonlinear effects in solids.

Main achievements are the following:

• Finding the exact multisoliton solutions of the Landau-Lifshitz equation for one-dimensional biaxial ferromagnet,
• Discovery of the oscillatory instability in soliton dynamics,
• Theoretical description of formation of multisoliton complexes and their coherent motion in strongly dispersive media,
• Finding the exact discrete multibreather and periodic solutions in integrable nonlinear lattices,
• Exact description of localized excitations and spin waves in anisotropic ferro- and antiferromagnets containing domain walls in the presence of a magnetic field.

Last five years activity and current interests:

Subjects of current investigations include dynamical properties of nonlinear excitations in condensed matter, especially soliton interaction and formation of multisoliton complexes in strongly dispersive media, investigation of their stability properties and internal motion, computer simulation of the nonstationary dynamics of soliton complexes; exact theoretical description of spin waves scattering by moving domain walls in anisotropic antiferromagnets in a magnetic field, exact solution of spectral problem for localized excitations in ferromagnetic chains containing spin nanoclusters, theory of the local negative magnetic permeability in nonlinear metamaterials and possibility of observation of breather excitations in such systems; exact description of collision processes of discrete breathers and nonlinear periodic waves in integrable models of anharmonic crystals and nonlinear transmission lines.

Educational activity:

• Professor of Theoretical Physics Department Named by Academician I.M. Lifshits in Kharkov National University from 2006 up to now. Personal page in Kharkov University:
• Supervisor of three PhD theses: two Doctors of Philosophy in theoretical physics and one in solid state physics.

Awards:

Certificates of Honour from Presidium of the NAS of Ukraine (2008, 2018).

List of XXI-century publications :

1. M.M. Bogdan, A.M. Kosevich, and G.A. Maugin. Soliton Complex Dynamics in Strongly Dispersive Medium. Wave Motion. V.34, No.1, 1-26 (2001).
2. M.M. Bogdan, C.E. Zaspel. Vortex Patterns in Layered Magnets with Magnetic and Nonmagnetic Impurities. Physica Status Solidi (a). V.189, No. 3, 983-988 (2002).
3. M.M. Bogdan and G.A. Maugin. Exact discrete breather solutions and conservation laws of lattice equations. Proc. Estonian Acad. Sci. Phys. Math. V.52, No.1, 76-84 (2003).
4. M.M. Bogdan, A.S. Kovalev, and E. Malyuta. Spectrum of nonlinear excitations of modulated nanoclusters. Low Temperature Physics. V. 31, No.7, 613-618 (2005).
5. M.M. Bogdan. The frustrated vortex in a two-dimensional antiferromagnet. Low Temperature Physics. V.31, No.8/9, 968-973 (2005).
6. O.V. Charkina, M.M. Bogdan. Internal Modes of Oscillations of Topological Solitons in Highly Dispersive Media. Uzhhorod University Scientific Herald. Series Physics. Iss. 17, 30-37 (2005).
7. S. Boscolo, S.A. Derevyanko, S.K. Turitsyn, A.S. Kovalev andM.M. Bogdan. Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem. Theoretical and Mathematical Physics. V. 144, No.2, 1117-1127 (2005).
8. S. Boscolo, S.A. Derevyanko, S.K. Turitsyn, A.S. Kovalev andM.M. Bogdan. Autosoliton propagation and mapping problem in optical fiber lines with lumped nonlinear devices. Phys. Rev. E. V.72, No.1 , 016601-1-016601-4 (2005).
9. O.V. Charkina, M.M. Bogdan. Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems SIGMA (Symmetry, Integrability and Geometry: Methods and Applications). V.2, No.047, 1-12 (2006).
10. O.V. Charkina, M.M. Bogdan. Processes of formation of soliton complexes and breathers in highly dispersive media. Uzhhorod University Scientific Herald. Series Physics. Iss.21, 196-204 (2007) [in Ukrainian]
11. L. Kroon, M.M Bogdan, A.S. Kovalev and E.Yu. Malyuta. Bifurcation picture and stability of gap and out-gap discrete solitons. Low Temperature Physics. V.33, No.5, 481-483 (2007).
12. M.M. Bogdan, O.V. Charkina. Dynamical features of bound states of topological solitons in highly dispersive low-dimensional systems Low Temperature Physics. V.33, No.12, 1073-1076 (2007).
13. M.M. Bogdan, O.V. Charkina. Dynamics and stability of solitons in the sine-Gordon models with a strong dispersion Nonlinear world. V.6, No.5-6, 324-333 (2008) [in Russian].
14. M.M. Bogdan, O.V. Charkina. Dynamics of bound soliton states in regularized dispersive equations. Low Temperature Physics. V.34, No 7, 564-570 (2008).
15. M.M. Bogdan and D.V. Laptev. Quasiclassical spectra of the solitons of the continual and discrete modified Korteweg - de Vries equations. Uzhhorod University Scientific Herald. Series Physics. Iss.24, 100-107 (2009) [in Ukrainian].
16. M.M. Bogdan, O.V. Charkina. Spin waves in easy-axis antiferromagnets with precessing domain walls Low Temperature Physics. V.40, N1, 84-90 (2014).
17. M.M. Bogdan, O.V. Charkina. Local negative magnetic permeability and possibility of observation of breather excitations in magnetic metamaterials Low Temperature Physics. V.40, N3, 234-238 (2014).
18. D.V. Laptev M.M. Bogdan. Nonlinear periodic waves solutions of the nonlinear self-dual network equations. Journal of Mathematical Physics. V.55, No.4, 042903-1-042903-22, (2014).
19. M.M. Bogdan and D.V. Laptev. Exact Description of the Discrete Breathers and Solitons Interaction in the Nonlinear Transmission Lines Journal of the Physical Society of Japan. V.83, No.6, 064007-1-064007-9 (2014).
20. O.V. Charkina, M.M. Bogdan Localized excitations and scattering of spin waves in ferromagnetic chains containing magnetic nanoclusters Low Temperature Physics. V.44, N7, 644-650 (2018).
21. M.M. Bogdan, V.I. Belan, O.V. Charkina. The effect of the magnetic field on the stability and excitation spectrum of spin nanoclusters in anisotropic ferromagnetic chains. Low Temperature Physics. V.44, N12, 1331-1340 (2018).
22. O.V. Charkina, M.M. Bogdan. Metastable breathers and local diamagnetism in two-dimensional nonlinear metamaterials. Low Temperature Physics. V.46, N7, 712-723 (2020).
23. M.M. Bogdan, O.V. Charkina. Generation of wave packets and breathers by oscillating kinks in the sine-Gordon system. Low Temperature Physics. V.47, N2, 155-165 (2021).
24. M.M. Bogdan, O.V. Charkina. Nonlinear oscillations of topological structures in the sine-Gordon systems Low Temperature Physics. V.47, N6, (2021).