\u0412\u0438\u043a\u043b\u0430\u0434\u0430\u0446\u044c\u043a\u0438\u0439 \u0434\u043e\u0441\u0432\u0456\u0434 <\/div><\/span>\n\t\t\t\t\t\t\t\n\t\t\t

\n\t\t\t\t

\n\t\t\t\t\t\t\t\t\t

Introduction to Inverse Spectral Problems; <\/span><\/li>
Partial Differential Equations; <\/span><\/li>
Riemann-Hilbert Problem and Nonlinear Equations; <\/span><\/li>
\u0423\u0437\u0430\u0433\u0430\u043b\u044c\u043d\u0435\u043d\u0456 \u0444\u0443\u043d\u043a\u0446\u0456\u0457<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t
Achievements and Scientific Activity <\/div><\/span>\n\t\t\t\t\t\t\t\n\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t
2020: State Prize in Science and Technology; <\/span><\/li>
2012: M.V. Ostrohradskyi Prize of the NAS of Ukraine<\/span><\/li><\/ul>
Grants:\u00a0<\/span><\/h4>
\u00abInitial-boundary value problems for nonlinear dispersive equations\u00bb (joint Ukrainian-Austrian research project 2025-2026, No. 0125U003485)<\/span><\/li>
Ukraina-NASTRAN cooperation project (2026-2028), no. 361083<\/span><\/li>
VUIAS fellowship 2025-2026<\/span><\/li>
NFDU Grant 2026-2028<\/span><\/li>
\u00a0<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t
\u041e\u0431\u0440\u0430\u043d\u0456 \u043d\u0430\u0443\u043a\u043e\u0432\u0456 \u043f\u0443\u0431\u043b\u0456\u043a\u0430\u0446\u0456\u0457 <\/div><\/span>\n\t\t\t\t\t\t\t\n\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t
Ya. Rybalko, D.Shepelsky, S.-F. Tian, The integrable nonlocal nonlinear Schr\u00f6dinger equation with oscillatory boundary conditions: Long-time asymptotics, Physica D 481 (2025), 134820.<\/span><\/li>
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.<\/span><\/li>
R. Barkov and D.Shepelsky, A\u00a0 Riemann\u2013Hilbert approach to solution of the\u00a0 modified focusing complex short pulse\u00a0 equation, Front. Appl. Math. Stat. 10 (2024), 1466965.<\/span><\/li>
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\u00a0 42, no. 16 (2024),\u00a0 5529-5536.<\/span><\/li>
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.<\/span><\/li>
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.<\/span><\/li>
Karpenko, D.Shepelsky and G.Teschl, A Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary, Monatshefte f\u00fcr Mathematik 201 (2023), 127-172.<\/span><\/li>
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.<\/span><\/li>
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.<\/span><\/li>
Ya. Rybalko and D.Shepelsky, Asymptotic stage of modulation instability for the nonlocal nonlinear Schr\u00f6dinger equation, Physica D 428 (2021) 133060.<\/span><\/li>
Ya. Rybalko and D.Shepelsky, Curved wedges in the long-time asymptotics for the integrable nonlocal nonlinear Schr\u00f6dinger equation, Stud. Appl. Math. 147, no. 3 (2021), 872-903.<\/span><\/li>
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.<\/span><\/li>
Ya. Rybalko and D.Shepelsky, Long-time asymptotics for the integrable nonlocal focusing nonlinear Schr\u00f6dinger equation for a family of step-like initial data, Commun. Math. Phys. 382 (2021), 87-121.<\/span><\/li>
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.<\/span><\/li>
Ya. Rybalko and D.Shepelsky, Long-time asymptotics for the nonlocal nonlinear Schr\u00f6dinger equation with step-like initial data, J. Differential Equations 270 (2021), 694-724.<\/span><\/li>
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.<\/span><\/li>
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.<\/span><\/li>
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.<\/span><\/li>
Ya. Rybalko and D.Shepelsky, Long-time asymptotics for the integrable nonlocal nonlinear Schr\u00f6dinger equation, J. Math. Phys. 60 (2019), 031504.<\/span><\/li>
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.<\/span><\/li>
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.<\/span><\/li>
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.<\/span><\/li>
A.Boutet de Monvel, D.Shepelsky and L.Zielinski, The short pulse equation by a Riemann-Hilbert approach, Lett. Math. Phys. 107 (2017), 1345\u20131373.<\/span><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t
Selected Conferences and Visits <\/div><\/span>\n\t\t\t\t\t\t\t\n\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t
2025\u00a0 \u00a0 XII International Skorobohatko Mathematical Conference, Lviv, Ukraine<\/span><\/li>
2024\u00a0 \u00a0 Bogolyubov Kyiv Conference \u201cProblems of Theoretical and Mathematical Physics\u201d, Ukraine<\/span><\/li>
2022 <\/span> SIAM Conference on Nonlinear Waves and Coherent Structures, Bremen, Germany<\/span><\/li>
2018\u00a0 <\/span> Differential Equations and Control Theory (DECT-2018), Kharkiv, Ukraine<\/span><\/li>
2016\u00a0 \u00a0 Spectral Theory, Differential Equations and Probability, Mainz, Germany<\/span><\/li>
2016\u00a0 \u00a0 Nordic Congress of Mathematicians, Stockholm, Sweden<\/span><\/li>
2015\u00a0 \u00a0 Mathematical Analysis and Scientific Computing, Taipei, Taiwan<\/span><\/li>
2013 Hamiltonian PDEs, Frobenius Manifolds and Deligne-Mumford Moduli Spaces, Trieste, Italy<\/span><\/li>
2011 Completely Integrable Systems and Applications, Vienna, Austria<\/span><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t
\u041d\u0430\u0443\u043a\u043e\u0432\u0456 \u0432\u0456\u0437\u0438\u0442\u0438 \u0442\u0430 \u043f\u0456\u0434\u0432\u0438\u0449\u0435\u043d\u043d\u044f \u043a\u0432\u0430\u043b\u0456\u0444\u0456\u043a\u0430\u0446\u0456\u0457 <\/div><\/span>\n\t\t\t\t\t\t\t\n\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t
University Paris-7; <\/span><\/li>
The Pennsylvania State University, USA; <\/span><\/li>
Cambridge University, UK; <\/span><\/li>
SISSA, Trieste, Italy; <\/span><\/li>
ACMAC, University of Crete, Greece; <\/span><\/li>
University of Littoral, Calais, France; <\/span><\/li>
Courant Institute of Mathematical Sciences, USA; <\/span><\/li>
University of Vienna, Austria; <\/span><\/li>
Aston University, Birmingham, UK; <\/span><\/li>
University of Ljubljana, Slovenia; <\/span><\/li>
University of Oslo, Norway; <\/span><\/li>
Seoul National University, Republic of Korea.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t\t
\n\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t $\"\"$ \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t $\"\"$ \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t $\"\"$ \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"
\u0428\u0435\u043f\u0435\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u0414\u043c\u0438\u0442\u0440\u043e \u0413\u0435\u043e\u0440\u0433\u0456\u0439\u043e\u0432\u0438\u0447 \u0427\u043b\u0435\u043d-\u043a\u043e\u0440\u0435\u0441\u043f\u043e\u043d\u0434\u0435\u043d\u0442 \u041d\u0410\u041d \u0423\u043a\u0440\u0430\u0457\u043d\u0438, \u0434\u043e\u043a\u0442\u043e\u0440 \u0444\u0456\u0437\u0438\u043a\u043e-\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0438\u0445 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0438\u0445 \u043d\u0430\u0443\u043a, \u043f\u0440\u043e\u0444\u0435\u0441\u043e\u0440(\u0437\u0430 \u0441\u0443\u043c\u0456\u0441\u043d\u0438\u0446\u0442\u0432\u043e\u043c) \u043a\u0430\u0444\u0435\u0434\u0440\u0438 […]<\/p>\n","protected":false},"author":17,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-3824","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/pages\/3824","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/comments?post=3824"}],"version-history":[{"count":28,"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/pages\/3824\/revisions"}],"predecessor-version":[{"id":4110,"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/pages\/3824\/revisions\/4110"}],"wp:attachment":[{"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/media?parent=3824"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}