Dmitry Shepelsky
 
Contact Information
 

Mailing Address
B. Verkin Institute for Low Temperature Physics and Engineering
47 Nauky Ave.
61103, Kharkiv, Ukraine

Office

 Mathematical division, Room 310

E-Mail

 shepelsky@yahoo.com shepelsky@ilt.kharkov.ua
Education and degrees

Habilitations

(1) Contributions à l'étude des propriétés spectrales et de scattering de la pro-
pagation des ondes électromagnétiques, Université Paris 7, France, 2000.
(2) The Riemann-Hilbert method in inverse problems and integrable equations,
ILTPE, Kharkiv, 2008 (Doctor of Sciences Thesis).

PhD Thesis

Inverse spectral problems for differential operators with discontinuities,
Kharkiv State University, 1992
(scientific adviser E.Khruslov, ILTPE, Kharkiv).

Post-graduate

ILTPE, Kharkiv (1988-1991).

Graduate

Kharkiv State University (1980-1985),
Diploma with honor in Mathematics, 1985.

Scopus ID: 35615520900

Web of Science ResearcherID: L-1559-2018

ORCID ID: 0000-0001-6616-5893

Research interests
• Inverse spectral analysis for ordinary differential and difference operators.
• Direct and inverse scattering theory.
• Nonlinear integrable PDE: inverse scattering transform, Riemann-Hilbert problem formalism, initial boundary valure problems, long-time asymptotics.
Employment
— since 2021: Head of Department of Geometry and Differential Equations, ILTPE, Kharkiv
— 2016-2021: professor, V.Karazin Kharkiv National University, Kharkiv
— 2010-2021: leading researcher, ILTPE, Kharkiv
— 1995-2010: senior researcher, ILTPE, Kharkiv
— 1992-1994: researcher, ILTPE, Kharkiv
— 1985-1992: junior researcher, ILTPE, Kharkiv
Teaching
— Riemann-Hilbert problems and applications to PDE, University Lille 1 (Fall 2018)
— Riemann-Hilbert problems and nonlinear equations, Kharkiv National University (Spring 2017, Spring 2018, Fall 2018)
— Inverse spectral problems, Kharkiv National University (Fall 2016, Fall 2017, Fall 2018)
— Partial differential equations, Kharkiv National University (Fall 2016, Fall 2017)
— Inverse scattering problems, University Paris 7 (Spring 2001, Spring 2002)
— Riemann-Hilbert problems and applications, University Paris 7 (Spring 2000)
Invitations
— Aston University (2017 - 2020)
— University of Littoral, Calais, France (2003, 2005, 2010, 2013, 2015, 2017)
— Institute of Mathematics Jussieu, University Paris-7 (1995, 1999, 2003-2013, 2015, 2016)
— Courant Institute of Mathematical Sciences, USA (2006 – 2012, 2015)
— University of Vienna, Austria (2014, 2019)
— ACMAC, University of Crete, Greece (2011, 2012)
— SISSA, Trieste, Italy (2011)
— Cambridge University, UK (2003)
— The Pennsylvania State University, USA (2001)
Referee Service
Referee services provided for the journals: Scientific Reports; Communications in Mathematical Physics; Communications in Mathematical Sciences; Communications in Nonlinear Science and Numerical Simulation; Physica D: Nonlinear Phenomena; Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences; Journal of Mathematical Analysis and Applications; Journal of Mathematical Physics; Journal of Physics A: Mathematical and Theoretical; Journal of Differential Equations; Journal of Physics Communications; Journal of Nonlinear Mathematical Physics; Inverse Problems; Nonlinearity; Chaos, Solitons and Fractals; Reports on Mathematical Physics; Physics Letters A; Complex Analysis and Operator Theory; Complex Variables and Elliptic Equations; Mathematical Methods in Applied Sciences; Mathematical Problems in Engineering; Mathematische Nachrichten; Funkcialaj Ekvacioj; Studies in Applied Mathematics; Mathematical Physics, Analysis and Geometry; Advances in Mathematical Physics; Advances in Mechanical Engineering; Analysis and Mathematical Physics; AIMS Mathematics; East Asian Journal on Applied Mathematics. .
Selected Talks
— 44-th European Conference on Optical Communication, Rome, Italy (2018)
— Equations and Control Theory (DECT 2018), Kharkiv, Ukraine (2018)
— Equations, Mathematical Physics and Applications, Cherkasy, Ukraine (2017)
— Nordic Congress of Mathematicians, Stockholm, Sweden (2016)
— Spectral Theory, Differential Equations and Probability, Mainz, Germany (2015)
— Mathematical Analysis and Scientific Computing, Taipei, Taiwan (2015)
— Analysis and Mathematical Physics, Kharkiv, Ukraine (2014, 2015, 2016, 2018)
— Hamiltonian PDEs, Frobenius Manifolds and Deligne-Mumford Moduli Spaces, Trieste, Italy (2013)
— Completely Integrable Systems and Applications, Vienna, Austria (2011)
— International Congress of Mathematicians (ICM 2010), Hyderabad, India (2010)
— Journees non lineaires - Journees Venakides, Paris, France (2010)
— Mathematics and Physics of Integrable Systems, Dijon, France (2009)
— Lyapunov Memorial Conference, Kharkiv, Ukraine (2007)
— International Congress of Mathematicians (ICM 2002), Beijing, Chine (2002)
— European Symposium on Numeric Methods in Electromagnetics, Toulouse, France (2002)
— International Congress of Mathematicians (ICM98), Berlin, Germany (1998)
— The Second Applied Mathematics Forum, Kyongju, Republic of Korea (1998)
— The First Applied Mathematics Forum, Sokcho, Republic of Korea (1997)
— Conference on Inverse Problems of Wave Propagation and Diffraction, Aix-les-Bains, France (1996)
Selected Publications
  1. A.Boutet de Monvel, J.Lenells and D. Shepelsky, The focusing NLS equation with step-like oscillating background: The genus 3 sector, Commun. Math. Phys. 390 (2022), 1081–1148.
  1. Y.Rybalko and D. Shepelsky, Asymptotic stage of modulation instability for the nonlocal nonlinear Schrödinger equation, Physica D 428 (2021), 133060.
  1. Y.Rybalko and D. Shepelsky, Curved wedges in the long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation, Stud Appl Math. 147 (2021), 872–903.
  1. S.Derevyanko, M.Balogun, O.Aluf, D. Shepelsky, and Ja.Prilepsky, Channel model and the achievable information rates of the optical nonlinear frequency division-multiplexed systems employing continuous b-modulation, Optics Express 29, no.5 (2021), 6384-6406.
  1. A.Boutet de Monvel, J.Lenells and D. Shepelsky, The focusing NLS equation with step-like oscillating background: scenarios of long-time asymptotics, Commun. Math. Phys. 383 (2021), 893-952.
  1. Y.Rybalko and D. Shepelsky, Long-time asymptotics for the integrable nonlocal focusing nonlinear Schrödinger equation for a family of step-like initial data, Commun. Math. Phys. 382 (2021), 87-121.
  1. Y.Rybalko and D. Shepelsky, Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data, J. Differential Equations 270 (2021), 694-724.
  1. Y.Rybalko and D. Shepelsky, Defocusing nonlocal nonlinear Schrödinger equation with step-like boundary conditions: long-time behavior for shifted initial data, Journal of Mathematical Physics, Analysis, Geometry 16, no. 4 (2020), 418-453.
  1. M.Kamalian, A. Vasylchenkova, D. Shepelsky, Ja.E. Prilepsky and S.K.Turitsyn, Full-spectrum periodic nonlinear Fourier transform optical communication through solving the Riemann-Hilbert problem, Journ. Lightwave Technology 38, no. 5 (2020), 3602-3615.
  1. D. Shepelsky, A. Vasylchenkova, Ja.E.Prilepsky and I.Karpenko, Nonlinear Fourier spectrum characterization of time-limited signals, IEEE Transactions on Communications 68, no. 5 (2020), 3024-3032.
  1. A.Boutet de Monvel, I.Karpenko and D. Shepelsky, A Riemann-Hilbert approach to the modified Camassa-Holm equation with nonzero boundary conditions, J. Math. Phys. 61 (2020), 031504.
  1. Y.Rybalko and D. Shepelsky, Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation, J. Math. Phys. 60 (2019), 031504.
  1. A.Boutet de Monvel, J.Lenells and D. Shepelsky, Long-time asymptotics for the Degasperis-Procesi equation on the half-line, Ann. Inst. Fourier 69, no. 1 (2019), 171-230.
  1. A. Vasylchenkova, J.E. Prilepsky, D. Shepelsky, and A. Chattopadhyay, Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation, Communications in Nonlinear Science and Numerical Simulation 68 (2019), 347-371.
  1. M. Kamalian, A. Vasylchenkova, J.E. Prilepsky, D. Shepelsky, and S.K.Turitsyn, Signal modulation and processing in nonlinear fibre channels by employing the Riemann-Hilbert Problem, Journ. Lightwave Technology 36, no. 24 (2018), 5714-5727.
  1. A. Vasylchenkova, J.E. Prilepsky, D. Shepelsky, and A. Chattopadhyay, Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation, Communications in Nonlinear Science and Numerical Simulation, (2019), 347-371
  1. V. Kotlyarov and D. Shepelsky, Planar unimodular Baker-Akhiezer function for the nonlinear Schrödinger equation, Annals of Mathematical Sciences and Applications, 2 (2017), 343-384.
  1. A.Boutet de Monvel, D. Shepelsky, and L.Zielinski, The short pulse equation by a Riemann-Hilbert approach, Lett. Math. Phys. 107 (2017), 1345–1373.
  1. A.Boutet de Monvel, D. Shepelsky, and L.Zielinski, A Riemann-Hilbert approach for the Novikov equation, SIGMA 12 (2016), 22 pp.
  1. S. Kamvissis, D. Shepelsky, and L. Zielinski, The Robin boundary condition and the shock problem for the focusing nonlinear Schrödinger equation, Journ. Nonlin. Math. Phys. 22, No. 3 (2015), 448–473.
  1. A.Boutet de Monvel and D. Shepelsky, The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach, J. Phys. A: Math. Theor. 48 (2015), 035204 (34pp).
  1. A.Its and D. Shepelsky, Initial boundary value problem for the focusing nonlinear Schrödinger equation with Robin boundary condition: half-line approach, Proc. R. Soc. A 469 (2013), 20120199
  1. A.Boutet de Monvel and D. Shepelsky, A Riemann-Hilbert approach for the Degasperis-Procesi equation, Nonlinearity 26 (2013), 2081-2107.
  1. A.Boutet de Monvel, V.Kotlyarov, and D. Shepelsky, Focusing NLS equation: long-time dynamics of step-like initial data, International Mathematics Research Notices (2011), no. 7, 1613-1653.
  1. A.Boutet de Monvel, V.Kotlyarov, D. Shepelsky and Ch. Zheng, Initial boundary value problems for integrable systems: towards the long time asymptotics, Nonlinearity 23 (2010), 2483-2499.
  1. A.Boutet de Monvel, A.Its, and D. Shepelsky, Painleve-type asymptotics for the Camassa-Holm equation, SIAM J. Math. Anal. 42 (2010), 1854-1873.
  1. A.Boutet de Monvel, V.Kotlyarov, and D. Shepelsky, Decaying long-time asymptotics for the focusing NLS equation with periodic boundary condition, International Mathematics Research Notices, No. 3 (2009), 547-577.
  1. A.Boutet de Monvel, A. Kostenko, D. Shepelsky, and G. Teschl, Long-time asymptotics for the Camassa-Holm equation, SIAM J. Math. Anal. 41 (2009), 1559-1588.
  1. A.Boutet de Monvel and D. Shepelsky, Riemann-Hilbert problem in the inverse scattering for the Camassa-Holm equation on the line, in: Probability, Geometry and Integrable Systems, Math. Sci. Res. Inst. Publ. 55, Cambridge Univ. Press, Cambridge, 2007, 53-75.
  1. A.Boutet de Monvel, A.Fokas ,and D. Shepelsky, Integrable nonlinear evolution equations on a finite interval, Commun. Math. Phys. 263 (2006), 133-172.
  1. A.Boutet de Monvel and D. Shepelsky, Initial boundary value problem for the mKdV equation on a finite interval, Annales de l'Institute Fourier, 54, no.5 (2004), 1477-1495.
  1. A.Boutet de Monvel, A.Fokas, and D. Shepelsky, Analysis of the global relation for the nonlinear Schrödinger equation, Lett. Math. Phys. 65, no.3 (2003), 199-212.
  1. D. Shepelsky, A Riemann-Hilbert problem for propagation of electromagnetic waves in an inhomogeneous, dispersive Omega waveguide, Math. Phys. Anal. Geom. 3, no.2 (2000), 179-193.
  1. D.Sheen and D. Shepelsky, Uniqueness in a frequency-domain inverse problem of a stratified uniaxial bianisotropic medium, Wave Motion, 31, no.4 (2000), 371-385.
  1. D.Sheen and D. Shepelsky, Inverse scattering problem for a stratified anisotropic slab, Inverse Problems, 15, no.2 (1999), 499-514.
  1. D.Sheen and D. Shepelsky, Uniqueness in simultaneous reconstruction of multiparameters of a transmission line, Progress in Electromagnetic Research, PIER 21 (1998), 153-172.
  1. A.Boutet de Monvel and D. Shepelsky, Direct and inverse scattering problem for a stratified nonreciprocal chiral medium, Inverse Problems, 13, no.2 (1997), 239-251.
  1. E.Khruslov and D. Shepelsky, Inverse scattering method in electromagnetic sounding theory, Inverse Problems, 10, no. 1 (1994), 1-37.
  1. D. Shepelsky, The inverse problem of reconstruction of the medium's conductivity in a class of discontinuous and creasing functions, Spectral Operator Theory and Related Topics, Advances in Soviet Mathematics, 19, ed. V.A.Marchenko, AMS, Providence, RI (1994), 209-232.