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Author: search.filters.author.Pelinovsky, EfimLanguage: search.filters.language.English

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    Wave packet dynamics in rotating fluids within the Benjamin–Ono–Ostrovsky equation
    (Elsevier BV, 2026-03-01)
    We investigate the evolution of algebraic solitons of the Benjamin–Ono (BO) equation and wave packets within the framework of the Benjamin–Ono–Ostrovsky (BOO) equation by combining asymptotic analysis with direct numerical simulations. The BOO model incorporates a low-frequency dispersive term that accounts for the effects of background rotation in a fluid. Through asymptotic expansion, we derive a cubic nonlinear Schrödinger (NLS) equation that governs the evolution of modulated wave trains and compare its predictions with numerical simulations of the full BOO equation. Theoretical and numerical results show good agreement for small-amplitude wave packets. Furthermore, near the boundary separating the modulationally stable and unstable regimes, the wave packets display pronounced broadening accompanied by enhanced amplitude attenuation. Finally, the evolution of BO algebraic solitons within the BOO framework is analyzed, revealing their gradual transformation into modulated wave packets.
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    FPTU recurrence within the Gardner equation
    (Springer Science and Business Media B.V., 2025-05-01)
    The study of Fermi–Pasta–Ulam–Tsingou (FPUT) recurrence is examined within the framework of the Gardner equation. The evolution of harmonic waves is investigated for both positive and negative cubic nonlinearities. It is observed that harmonic waves undergo fission into solitons, which then interact with each other. For positive cubic nonlinearity, recurrence occurs periodically over time for weak and intermediate nonlinearities. However, as the dispersion becomes weaker, this phenomenon ceases to occur. Conversely, for negative cubic nonlinearity, recurrence is also observed for weak and intermediate nonlinearities, but it lacks a well-defined temporal period.
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