Breather’s Properties within the Framework of the Modified Korteweg–de Vries Equation

Didenkulova, Ekaterina; Pelinovsky, Efim

doi:10.3390/sym12040638

Cited by 9 publications

(3 citation statements)

References 35 publications

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“…Additionally, a similar research was performed to the dynamics of breather (periodic pulsating wave packet) gas, which also shows that breather interactions may produce the RWs on the surface of deep water [32,33].…”

Section: Introductionmentioning

confidence: 93%

Characteristics of soliton gas with the strongest pairwise soliton interactions in the focusing Gardner equation

Zhang,

Xu,

Yang

et al. 2024

Preprint

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For the focusing Gardner equation, we investigate the dynamics of soliton gas (SG) incorporating the strongest pairwise soliton interactions that achieve the maximum attainable amplification AI = 2. In our simulated SG, the interactions of positive solitons overtaking negative ones are dominant because the velocities of most of positive solitons are larger than those of negative ones in the initial distribution. As the number of bipolar soliton pairs with AI = 2 increases, the third moment decrease in absolute while the fourth moment increases. Meanwhile, the maximum values in the global wave field increase significantly while the minimum values exhibit a relatively modest increase, owing to the generation of many high positive transient waves during interactions, as compared to the limited production of high negative transient waves. Also, an obvious elevation in the tails of global probability density functions is observed for positive wave amplitudes, which indicates an increase of the number of extreme events in the wave field. In addition, the rogue wave (RW) occurrence probability does not increase but rather decreases, in contrast to the situation in the integrable turbulence. Our findings may be useful for realizing some controllable experiments of the SGs in water waves. PACS: 05.45.Yv; 02.30.Ik; 47.35.Fg.

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Section: Introductionmentioning

confidence: 93%

Characteristics of soliton gas with the strongest pairwise soliton interactions in the focusing Gardner equation

Zhang,

Xu,

Yang

et al. 2024

Preprint

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“…The significant increase in wave moments was observed in the dominant interaction region of two waves (Figure 4). The initial values of non-interacting waves can be found analytically [41]. The third moment of symmetrical individual breather is equal to zero.…”

Section: Moments Of the Wave Fieldsmentioning

confidence: 99%

“…While the quadratic nonlinearity is much smaller than the cubic one, the Gardner equation can be reduced to the modified KdV equation with the exact soliton and breather solutions [39,40]. A breather has more difficult dynamics than a soliton in some sense [41].…”

Section: Introductionmentioning

confidence: 99%

Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework

Didenkulova

Pelinovsky

2020

Symmetry

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Pairwise interactions of particle-like waves (such as solitons and breathers) are important elementary processes that play a key role in the formation of the rarefied soliton gas statistics. Such waves appear in different physical systems such as deep water, shallow water waves, internal waves in the stratified ocean, and optical fibers. We study the features of different regimes of collisions between a soliton and a breather in the framework of the focusing modified Korteweg–de Vries equation, where cubic nonlinearity is essential. The relative phase of these structures is an important parameter determining the dynamics of soliton–breather collisions. Two series of experiments with different values of the breather’s and soliton’s relative phases were conducted. The waves’ amplitudes resulting from the interaction of coherent structures depending on their relative phase at the moment of collision were analyzed. Wave field moments, which play a decisive role in the statistics of soliton gases, were determined.

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Characteristics of soliton gas with the strongest pairwise soliton interactions in the focusing Gardner equation

Zhang,

Xu,

Yang

et al. 2024

Nonlinear Dyn

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Breather’s Properties within the Framework of the Modified Korteweg–de Vries Equation

Cited by 9 publications

References 35 publications

Characteristics of soliton gas with the strongest pairwise soliton interactions in the focusing Gardner equation

Characteristics of soliton gas with the strongest pairwise soliton interactions in the focusing Gardner equation

Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework

Characteristics of soliton gas with the strongest pairwise soliton interactions in the focusing Gardner equation

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