Two-soliton interaction as an elementary act of soliton turbulence in integrable systems

Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of...

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Bibliographic Details
Published in:Physics letters. A 2013-01, Vol.377 (3-4), p.272-275
Main Authors: Pelinovsky, E.N., Shurgalina, E.G., Sergeeva, A.V., Talipova, T.G., El, G.A., Grimshaw, R.H.J.
Format: Article
Language:English
Subjects:
Dynamical systems
Fluid dynamics
Fluid flow
KdV equation
Mathematical analysis
Nonlinear dynamics
Soliton
Solitons
Turbulence
Turbulent flow
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Summary:Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg–de Vries (KdV) equation. While the first two moments are integrals of the KdV evolution, the 3rd and 4th moments undergo significant variations in the dominant interaction region, which could have strong effect on the values of the skewness and kurtosis in soliton turbulence. ► Two-soliton interactions define the structure of the KdV soliton turbulence. ► The 3rd and 4th moments of the KdV two-soliton are not conserved. ► Their variations lead to the decrease of the skewness and kurtosis.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2012.11.037