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Item type:Publication, Auto-resonance process under the interaction of solitons with external force and dissipation(Elsevier Ltd, 2024-12-01)Algebraic soliton interactions with an external force in the presence of Reynolds viscosity is investigated. In the absence of an external force, the soliton amplitude decays over time. However, when an external force is introduced, it acts as a restoring force, and in some cases, the soliton's amplitude is preserved. A dynamical system that governs the soliton amplitude and its crest position is obtained assuming a weak force and weak viscosity. For an external force with a Gaussian shape, the dynamical system has two equilibrium points, namely, a saddle and a stable spiral. Asymptotic results are compared with direct numerical simulations, and a strong qualitative agreement is observed. The stable spiral predicted by the asymptotic theory is stable in the sense that soliton solutions with a chosen amplitude and crest position near the spiral point are attracted to it, preserving their amplitude and location. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Solitons in dissipative systems subjected to random force within the Benjamin–Ono type equation(Elsevier Ltd, 2024-10-01)Solitary wave dynamics is investigated under the assumption of small dissipation and an external random force. Through a change of variables, the problem becomes homogeneous, allowing for the derivation of asymptotic algebraic soliton solutions. This change of variables makes the randomness manifest primarily on the soliton phases. Consequently, the averaged soliton field and the statistical moments can be computed analytically, assuming that the phase follows a uniform distribution. In the absence of Reynolds dissipation, we show that the soliton-averaged field tends to spread and dampen as the dispersion increases. In addition, in the presence of Reynolds dissipation, we demonstrate that algebraic solitons can transition between thick and thin soliton states. Moreover, when there is viscosity in the upper moving layer, the averaged soliton field exhibits a dynamic evolution from soliton to thick soliton to soliton, contingent upon the parameter settings. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Nonlinear random wave fields within a Boussinesq system(Elsevier B.V., 2024-09-28)The dynamics of nonlinear random fields is important for understanding wave turbulence. In this work, we use a Boussinesq system to examine the distinctions between unidirectional and bidirectional waves. Our study demonstrates that in both scenarios, the wave spectra reach a stationary state. Moreover, we show that the occurrence of rogue waves is more probable in the unidirectional case. In the unidirectional case, the probability distribution of wave crests exceeds the one predicted by the Rayleigh distribution once the spectra reach the stationary state. Conversely, in the bidirectional case, the opposite trend is observed. The discovery of various types of rogue waves, including massive wave trains commonly known in the literature as “two sisters” and “three sisters” are found. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Wave fields under the influence of a random-driven force: The Burgers equation(Elsevier B.V., 2024-12-15)In this work, we examine the classical Burgers equation and investigate the effects of a random force on the wave field. Two scenarios are considered: the impact of a random force on different wave fields within the viscous Burgers equation and the effect of a periodic random force in the inviscid Burgers equation. For the first case, we demonstrate that the random force primarily causes wave fronts to increase or decrease depending on the dispersion parameter. For an initially deformed sinusoidal wave, the external force causes the mean wave field to spread out and dampen over time. The Cole-Hopf transformation is also used to obtain asymptotically the averaged wave field in certain regimes. For the inviscid problem, we assume the random force to be periodic with random phase to show that the mean wave field corresponds to the solution of the classical inviscid Burgers equation without external forces. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Wave evolution within the cubic vortical Whitham equation(Elsevier BV, 2024-12-26)In this work, we study the evolution of disturbances within the framework of the Cubic Vortical Whitham (CV-Whitham) equation, considering both positive and negative cubic nonlinearities. This equation plays important role for description of the wave processes in the presence of shear flows. We find well-formed breather-type structures arising from the evolution of depression disturbances with positive cubic nonlinearity. For elevation disturbances, the results are two-fold. When the cubic nonlinearity is negative, we show that the CV-Whitham equation and the Gardner equation are qualitatively similar, differing only by a small phase lag due to differences in the dispersion term. However, with positive cubic nonlinearity, the differences between the solutions become more pronounced, with the CV-Whitham equation producing sharper waves that suggest the onset of wave breaking. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Нерегулярная динамика внутренних волн в слабо стратифицированной жидкости в модели уравнения Бенджамина-Оно с вязкостью(Springer Science+Business Media, 2025-06-30)Исследуется сложная динамика узкополосных волновых полей, описываемых уравнением Бенджамина-Оно с вязкостью - моделью, имеющей важное значение в гидродинамике. С помощью детального численного моделирования проведен анализ влияния вязкости Рейнольдса на статистические моменты, энергетические спектры и вероятности возникновения экстремальных внутренних волн. В частности, показано, что в вязких жидкостях могут возникать волны-убийцы небольшой амплитуды.15 - Some of the metrics are blocked by yourconsent settings
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, Wave dynamics within the Whitham-Ostrovsky equation(Springer Science+Business Media, 2026-06-01)In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution. The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render plane-wave solutions modulationally unstable. Direct numerical simulations confirm that, within the unstable region, wave packets undergo a pronounced compression, consistent with the self-focusing mechanism of the focusing NLS equation. In contrast, in the modulationally stable region, the wave packet progressively broadens in space while its peak amplitude decreases, as the wave energy is redistributed over an increasingly wider spatial interval. We further examine how solitary-wave solutions of the Whitham equation are modified within the WO framework, where they evolve into localized wave packets due to the presence of the rotating term. In addition, we investigate the dynamics of solitary waves in the anomalous dispersion regime. These solutions are computed numerically and evolved under the full time-dependent equation, revealing that their interactions are inelastic, with noticeable generation of dispersive radiation and an increase in the amplitude of the larger solitary wave. Although such interactions could, in principle, promote the emergence of a “soliton champion” or even a freak-wave–type structure after repeated collisions, the progressive steepening of the solitary waves alters this scenario. Numerical simulations indicate that, instead of forming a persistent dominant soliton, the wave profile continues to sharpen until the onset of wave breaking occurs. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Spring–mass behavior of solitons under the influence of an external force field within the modified Korteweg–de Vries equation(Elsevier BV, 2025-07-01)We investigate the interaction of solitons with an external periodic field within the framework of the modified Korteweg–de Vries (mKdV) equation. In the case of small perturbation a simple dynamical system is used to describe the soliton behavior. Equilibrium points of this dynamical system are computed when the external force travels at a constant speed. Assuming that the external force moves with sinusoidal speed, we demonstrate that the soliton behavior is qualitatively similar to the constant-speed case. Besides, a resonant frequency is derived from the asymptotic theory without using the classical broad force approximation. The results obtained from the dynamical system are compared with fully nonlinear direct numerical simulations, which reveal that the soliton solution exhibits spiral-like behavior in the soliton amplitude versus soliton phase space. Moreover, when the external force oscillates at the resonant frequency, the trajectories in the soliton phase versus soliton amplitude exhibit chaotic behavior.2 - 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