Solitons Interactions

Soomere, Tarmo

doi:10.1007/978-0-387-30440-3_507

Cited by 11 publications

(6 citation statements)

References 150 publications

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“…These effects may be particularly pronounced in the case of ship wakes that often approach seawalls or breakwaters from other directions than wind waves do (Soomere, 2007). The contribution of CENS into the study of soliton interactions was recognized by an invitation to summarize the developments for a recent encyclopaedia of complexity and systems science (Soomere, 2009).…”

Section: Water Waves and Turbulencementioning

confidence: 99%

EDITORIAL. Special issue devoted to the International Conference on Complexity of Nonlinear Waves. Highlights in the research into complexity of nonlinear waves

Engelbrecht¹,

Berezovski²,

Soomere³

2010

Proc. Estonian Acad. Sci.

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We reflect highlights of studies into a variety of phenomena reflecting the complexity of underlying nonlinear processes in a selection of research disciplines in the Centre of Nonlinear Studies (CENS), presented in the International Conference on Complexity of Nonlinear Waves, 5-7 October 2009, Tallinn, Estonia. We emphasize the similarity of mathematical description of and potential synergy arising from complementary studies in general soliton science, wave propagation in microstructured and functionally graded materials, related inverse problems, issues of nondestructive testing, weak resonant interactions of water waves, wave transformation and run-up, soliton interactions in shallow water, and selected problems of passive scalar turbulence.

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Section: Water Waves and Turbulencementioning

confidence: 99%

EDITORIAL. Special issue devoted to the International Conference on Complexity of Nonlinear Waves. Highlights in the research into complexity of nonlinear waves

Engelbrecht¹,

Berezovski²,

Soomere³

2010

Proc. Estonian Acad. Sci.

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“…For example, in many cases the total amplitude of the superposed solitons is less than the sum of each individual amplitude, but each amplitude is restored after the interaction (see figure 16.2). The interaction often generates a phase shift, a change of position compared to what would be the position of the solitons if the interaction did not occur (for more details, see Soomere 2011). Depending on the particular type of functional genidentity that is discussed, these characteristics of the interaction will or will not allow us to assert that the solitons emerging from the interaction are the same as the ones entering into it.…”

Section: Materials Genidentity 1) Continuity Of Changementioning

confidence: 99%

“…Temporal evolution of Korteweg-de Vries solitons described by the two--soliton solution u(x, t) = 12 * (3 + 4 cosh(2x − 8t) + cosh(4x − 64t))/ ([3 cosh(x − 28t) + cosh(3x − 36t)] 2 )(Soomere 2011(Soomere , 1583. Note the nonadditivity of amplitudes during interaction With kind permission from Springer Science and Business Media.…”

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confidence: 99%

To Be Continued

Guay¹,

Pradeu²

2015

Individuals Across the Sciences

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“…In many of these applications, the study of solitary waves is of particular importance, as these objects move rapidly and can transfer large amounts of energy [10]. For example, internal solitary waves-frequently imaged via aerial photography [14,15]-can have both small-scale impacts on deep water objects [16] and large-scale effects on climates and currents [10]. Consequently, a number of recent studies have examined the interactions of solitons with a changing background flow in the context of nonlinear, dispersive systems in one space and one time dimension (referred to as (1+1)-dimensional), including the Korteweg-de Vries (KdV) equation [17,18], the focusing nonlinear Schrödinger (NLS) equation [12,19], the defocusing NLS equation [13], and the conduit equation [18,20].…”

Section: Introductionmentioning

confidence: 99%

Oblique interactions between solitons and mean flows in the Kadomtsev-Petviashvili equation

Ryskamp,

Hoefer,

Biondini

2020

Preprint

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The interaction of an oblique line soliton with a one-dimensional dynamic mean flow is analyzed using the Kadomtsev-Petviashvili II (KPII) equation. Building upon previous studies that examined the transmission or trapping of a soliton by a slowly varying rarefaction or oscillatory dispersive shock wave in one space and one time dimension, this paper allows for the incident soliton to approach the changing mean flow at a nonzero oblique angle. By deriving invariant quantities of the soliton-mean flow modulation equations-a system of three (1+1)-dimensional quasilinear, hyperbolic equations for the soliton and mean flow parameters-and positing the initial configuration as a Riemann problem in the modulation variables, it is possible to derive quantitative predictions regarding the evolution of the line soliton within the mean flow. It is found that the interaction between an oblique soliton and a changing mean flow leads to several novel features not observed in the (1+1)dimensional reduced problem. Many of these interesting dynamics arise from the unique structure of the modulation equations that are nonstrictly hyperbolic, including a well-defined multivalued solution interpreted as a solution of the (2+1)-dimensional soliton-mean modulation equations, in which the soliton interacts with the mean flow and then wraps around to interact with it again. Finally, it is shown that the oblique interactions between solitons and dispersive shock wave solutions for the mean flow give rise to all three possible types of 2-soliton solutions of the KPII equation. The analytical findings are quantitatively supported by direct numerical simulations.

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Solitons Interactions

Cited by 11 publications

References 150 publications

EDITORIAL. Special issue devoted to the International Conference on Complexity of Nonlinear Waves. Highlights in the research into complexity of nonlinear waves

EDITORIAL. Special issue devoted to the International Conference on Complexity of Nonlinear Waves. Highlights in the research into complexity of nonlinear waves

To Be Continued

Oblique interactions between solitons and mean flows in the Kadomtsev-Petviashvili equation

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