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Item type:Publication, Wave packet dynamics within the modular Schamel equation(Elsevier BV, 2026-04-01)In this article, we investigate the evolution of long waves and the dynamics of wave packets governed by the modular Schamel equation. We show that the wave field disintegrates into solitary waves of both polarities and recurrence is not observed. Their interactions substantially amplify the wave field and, over long times and large domains, can trigger the formation of freak waves. Furthermore, under the assumption of weak nonlinearity, we seek wave packet solutions of the Schamel equation and derive a generalized nonlinear Schrödinger (gNLS) envelope equation, which inherits the same nonlinearity as the Schamel equation. In the parameter regime of interest, the gNLS supports only bright solitons, which inherit the Schamel solitary-wave profile (up to scaling). Additionally, the derived bright soliton was examined as an initial-value problem for the modular Schamel equation, where its numerical stability was confirmed, showing good agreement with the theoretical predictions.Scopus© Citations 1 1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, 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.1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, KdV-like soliton gas: similarity and difference in integrable and non-integrable models(Elsevier BV, 2025-11-01)A comparison of the statistical characteristics of a rarefied soliton gas is carried out within the framework of integrable and non-integrable equations from the Korteweg-de Vries (KdV) hierarchy. As examples, multi-soliton solutions of the modified KdV equation, and the modular Schamel equation are considered. A common property of the dynamics of bipolar solitons is the formation of rogue waves, which do not occur in unipolar gases. The fourth moment of the wave field (kurtosis) increases compared to the initial value in the case of a bipolar gas, and decreases for a unipolar gas. In the case of integrable KdV equations, the characteristics of the soliton gas reach a stationary level, while in non-integrable equations they remain functions of time. The inelastic transfer of energy from small solitons to large ones occur, and large waves become “more extreme” against the background of small solitons. The tendency of the occurrence of an anomalously large wave (soliton - champion) in non-integrable systems are discussed.1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Dynamics of Irregular Wave Fields in the Schamel Equation Framework(Pleiades Publishing, 2025-02-01)The present paper is devoted to the study of the dynamics of narrowband wave fields within the nonintegrable Schamel equation, which plays an important role in plasma physics, wave dynamics in metamaterials, and electrical circuits. A Monte Carlo approach is used to obtain a large number of random independent realizations of the wave fields, allowing for an investigation of the evolution of the following statistical characteristics: spectra, moments, and distribution functions. The simulations are conducted for different values of the Ursell number (the ratio of nonlinearity to dispersion) to study the impact of nonlinearity and dispersion on the processes under consideration. The features of freak waves appeared in the random wave fields are discussed.1