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Language: search.filters.language.EnglishSubject: 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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    Soliton dynamics under the influence of an external force and induced-damped terms within the modified Korteweg-de Vries equation
    (Springer Science+Business Media, 2026-01-01)
    The interaction of a solitary wave with an external force is studied within the framework of a modified Korteweg-de Vries equation, accounting for viscosity and damping. Using asymptotic methods, a dynamical system is derived to describe the amplitude and phase of the solitary wave. A bifurcation analysis of this system is presented, depending on the parameters characterizing viscosity and flow, and the conditions for the trapping of the solitary wave by the external force are examined. The obtained asymptotic results are compared with direct numerical simulations. The asymptotic and numerical results agree for all types of equilibrium points in the dynamical system.
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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.