Науково-педагогічний персонал

Шепельський Дмитро Георгійович

Член-кореспондент НАН України, доктор фізико-математичних математичних наук, професор(за сумісництвом) кафедри фундаментальної математики. Основне місце роботи: завідувач відділом диференціальних рівнянь і геометрії Фізико-технічного інституту низьких температур ім. Б.І. Вєркіна НАН України

Habilitation, University Paris-7 Denis Diderot

  • Диференціальні рівняння з частинними похідними

Посилання на сторінки в наукових мережах:

  • Вступ до обернених спектральних задач;

  • Диференціальні рівняння з частинними похідними;

  • Задача Рімана-Гільберта і нелінійні рівняння;

  • Узагальнені функції

  • 2020: Державна премія з науки і техніки;

  • 2012: Премія М.В. Остроградського НАН України

Гранти: 

  • «Початково-крайові задачі для нелінійних дисперсійних рівнянь» (спільний українсько-австрійський науково-дослідний проєкт 2025-2026, № 0125U003485)
  • Ukraina-NASTRAN cooperation project (2026-2028), no. 361083
  • VUIAS fellowship 2025-2026
  • Грант НФДУ 2026-2028
  •  
  1. Ya. Rybalko, D.Shepelsky, S.-F. Tian, The integrable nonlocal nonlinear Schrödinger equation with oscillatory boundary conditions: Long-time asymptotics, Physica D 481 (2025), 134820.
  2. A. Boutet de Monvel, J.Lennels and D.Shepelsky, The focusing NLS equation with step-like oscillating background: asymptotics in a transition zone, J. Differential Equations 429 (2025), 747-801.
  3. R. Barkov and D.Shepelsky, A  Riemann–Hilbert approach to solution of the  modified focusing complex short pulse  equation, Front. Appl. Math. Stat. 10 (2024), 1466965.
  4. S. Bogdanov, D.Shepelsky, M. Kamalian-Kopae, A. Vasylchenkova and J. E. Prilepsky, Finite-Genus Solutions-Based Optical Communication With the Riemann-Hilbert Problem Transmitter and a Convolutional Neural Network Receiver, Journal of Lightwave Technology  42, no. 16 (2024),  5529-5536.
  5. D.Shepelsky, I. Karpenko, S. Bogdanov and Ja.E. Prilepsky, Periodic finite-band solutions to the focusing nonlinear Schrodinger equation by the Fokas method: inverse and direct problems, Proc.R.Soc.A 480 (2024), 20230828.
  6. S. Bogdanov, D.Shepelsky, A. Vasylchenkova, E.Sedov, P.J.Freire, S.K.Turitsin and J.E.Prilepsky, Phase computation for the finite-genus solutions to the focusing nonlinear Schrodinger equation using convolutional neural networks, Communications in Nonlinear Science and Numerical Simulation 125 (2023), 107311.
  7. Karpenko, D.Shepelsky and G.Teschl, A Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary, Monatshefte für Mathematik 201 (2023), 127-172.
  8. Ya. Rybalko and D.Shepelsky, Global conservative solutions of the nonlocal NLS equation beyond blow-up, Discrete and Continuous Dynamical Systems 43, No. 2 (2023), 860-894.
  9. A. Boutet de Monvel, J.Lennels and D.Shepelsky, The focusing NLS equation with step-like oscillating background: The genus 3 sector, Commun. Math. Phys. 390 (2022), 1081-1148.
  10. Ya. Rybalko and D.Shepelsky, Asymptotic stage of modulation instability for the nonlocal nonlinear Schrödinger equation, Physica D 428 (2021) 133060.
  11. Ya. Rybalko and D.Shepelsky, Curved wedges in the long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation, Stud. Appl. Math. 147, no. 3 (2021), 872-903.
  12. A. Boutet de Monvel, J.Lennels and D.Shepelsky, The focusing NLS equation with step-like oscillating background: scenarios of long-time asymptotics, Commun. Math. Phys. 383 (2021), 893-952.
  13. Ya. 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.
  14. 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.
  15. Ya. 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.
  16. 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.
  17. M.Kamalian, A.Vasylchenkova, Ja.E. Prilepsky, D.Shepelsky and S.K.Turitsyn, Full-spectrum periodic nonlinear Fourier transform optical communication through solving the Riemann-Hilbert problem, Journ. Lightwave Technology 38, no.14 (2020), 3602-3615.
  18. 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.
  19. Ya. Rybalko and D.Shepelsky, Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation, J. Math. Phys. 60 (2019), 031504.
  20. 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.
  21. M. Kamalian, A. Vasylchenkova, D. Shepelsky, J. E. Prilepsky, 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.
  22. V.Kotlyarov and D.Shepelsky, Planar unimodular Baker-Akhiezer function for the nonlinear Schrodinger equation, Annals of Mathematical Sciences and Applications, 2 (2017), 343-384.
  23. 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. 2025    XII International Skorobohatko Mathematical Conference, Lviv, Ukraine
  2. 2024    Bogolyubov Kyiv Conference “Problems of Theoretical and Mathematical Physics”, Ukraine
  3. 2022 SIAM Conference on Nonlinear Waves and Coherent Structures, Bremen, Germany
  4. 2018  Differential Equations and Control Theory (DECT-2018), Kharkiv, Ukraine
  5. 2016    Spectral Theory, Differential Equations and Probability, Mainz, Germany
  6. 2016    Nordic Congress of Mathematicians, Stockholm, Sweden
  7. 2015    Mathematical Analysis and Scientific Computing, Taipei, Taiwan
  8. 2013    Hamiltonian PDEs, Frobenius Manifolds and Deligne-Mumford Moduli Spaces, Trieste, Italy
  9. 2011    Completely Integrable Systems and Applications, Vienna, Austria
  • University Paris-7;
  • The Pennsylvania State University, USA;
  • Cambridge University, UK;
  • SISSA, Trieste, Italy;
  • ACMAC, University of Crete, Greece;
  • University of Littoral, Calais, France;
  • Courant Institute of Mathematical Sciences, USA;
  • University of Vienna, Austria;
  • Aston University, Birmingham, UK;
  • University of Ljubljana, Slovenia;
  • University of Oslo, Norway;
  • Seoul National University, Republic of Korea.