Yan Rybalko

• Rybalko, Yan (2026). Riemann–Hilbert approach for the nonlocal modified Korteweg–de Vries equation with a step-like oscillating background. Letters in Mathematical Physics. ISSN 0377-9017. 116(4). doi: 10.1007/s11005-026-02119-y. Fulltekst i vitenarkiv
• Rybalko, Yan; Shepelsky, Dmitry & Tian, Shou-Fu (2025). The integrable nonlocal nonlinear Schrödinger equation with oscillatory boundary conditions: Long-time asymptotics. Physica D : Non-linear phenomena. ISSN 0167-2789. 481. doi: 10.1016/j.physd.2025.134820. Fulltekst i vitenarkiv
• Karlsen, Kenneth Aksel Hvistendahl & Rybalko, Yan (2025). Global semigroup of conservative weak solutions of the two-component Novikov equation. Nonlinear Analysis: Real world applications. ISSN 1468-1218. 86. doi: 10.1016/j.nonrwa.2025.104393. Fulltekst i vitenarkiv
• Karlsen, Kenneth Aksel Hvistendahl & Rybalko, Yan (2024). On the well-posedness of the Cauchy problem for the two-component peakon system in Ck∩Wk,1. Zeitschrift für Angewandte Mathematik und Physik. ISSN 0044-2275. 75(3). doi: 10.1007/s00033-024-02246-3. Fulltekst i vitenarkiv
• Karlsen, Kenneth Aksel Hvistendahl & Rybalko, Yan (2024). On the well-posedness of a nonlocal (two-place) FORQ equation via a two-component peakon system. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 529(1). doi: 10.1016/j.jmaa.2023.127601. Fulltekst i vitenarkiv Vis sammendrag

  We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By interpreting this equation as a special case of a two-component peakon system (exhibiting a cubic nonlinearity), we convert the Cauchy problem into a system of ordinary differential equations in a Banach space. Using this approach, we are able to demonstrate local well-posedness in the Sobolev space H8 where s > 5/2. We also establish the continuity properties for the data-to-solution map for a range of Sobolev spaces. Finally, we briefly explore the relationship between the two-component system and the bi-Hamiltonian AKNS hierarchy.

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