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Author: search.filters.author.Efim PelinovskySubject: search.filters.subject.Soliton

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    Soliton dynamics in random fields: The Benjamin-Ono equation framework
    (Elsevier BV, 2025-08-01)
    Algebraic soliton interactions with a periodic or quasi-periodic random force are investigated via the Benjamin-Ono equation, which models internal waves in a two-layer fluid. The random force is modeled as a Fourier series with a finite number of modes and random phases uniformly distributed, while its frequency spectrum has a Gaussian shape centered at a peak frequency. The expected value of the averaged soliton wave field is computed asymptotically and compared with numerical results, with a strong agreement shown. We identify parameter regimes where the averaged soliton field splits into two steady pulses and a regime where the soliton field splits into two solitons traveling in opposite directions. In the latter case, the averaged soliton speeds are variable. In both scenarios, the soliton field is damped by the external force. Additionally, we identify a regime where the averaged soliton exhibits the following behavior: it splits into two distinct solitons and then recombines to form a single soliton. This motion is periodic over time.
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    Emergence of champion solitons from two-solitary-wave interactions in the fourth-order generalized Korteweg–de Vries equation
    (Elsevier BV, 2026-07-01)
    Two-solitary-wave interactions are investigated within the fourth-order generalized Korteweg–de Vries equation. This equation is closely related to the classical Korteweg–de Vries equation but includes a quartic nonlinear term. We show that, although collisions between two solitary waves are not perfectly elastic, only a small amount of radiation is generated during the interaction. This allows a clear characterization of the collision type based on the number of local maxima observed during the interaction, following the Lax geometric categorization. Our results indicate that, in contrast to several non-integrable systems such as the Schamel equation and Whitham-type equations, the collision type depends solely on the ratio of the initial solitary-wave amplitudes. Moreover, after the interaction, the larger solitary wave increases its amplitude while the smaller one decreases. This behavior suggests that extreme, or freak waves or champion solitons may arise from the interaction of multiple solitary waves.
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    Asymptotic and numerical study to the damped Schamel equation
    (National Research Ogarev Mordovia State University, 2025-01-01)
    Analytical and numerical solutions of the damped Schamel equation, describing the dynamics of ion-acoustic waves in magnetized plasma, are presented. A small parameter is introduced in the equation before the dissipative term, ensuring that in its absence the solution reduces to a solitary wave (soliton). The asymptotic method employed for solving the equation is a variant of the Krylov-Bogolyubov-Mitropolsky multiple-scale technique. In the first-order approximation, the solution is described by a traveling solitary wave with slowly varying parameters. The second-order approximation yields the evolution laws for the soliton's amplitude and phase as functions of «slow» time. Additionally, exact integral conservation laws (mass and energy of the wave field), derived directly from the original damped Schamel equation, are utilized. These integrals allow estimating the soliton's radiative losses, particularly the mass of the so-called tail formed behind the soliton due to dissipation. Direct numerical solutions of the original equation, obtained via a pseudospectral method, confirm the asymptotic laws governing the soliton's amplitude decay caused by dissipation. Another limiting case - strong dissipation (dominant over nonlinearity and dispersion), is also investigated, demonstrating that the soliton decays as a linear impulse, which is validated numerically.
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