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

E. N. Pelinovsky; E. G. Shurgalina; A. V. Sergeeva; T. G. Talipova; G. A. El; R. H.J. Grimshaw

doi:10.1016/j.physleta.2012.11.037

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

E. N. Pelinovsky, E. G. Shurgalina, A. V. Sergeeva, T. G. Talipova, G. A. El^*, R. H.J. Grimshaw

^*Corresponding author for this work

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Abstract

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.

Original language	English
Pages (from-to)	272-275
Number of pages	4
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	377
Issue number	3-4
Early online date	19 Nov 2012
DOIs	https://doi.org/10.1016/j.physleta.2012.11.037
Publication status	Published - 3 Jan 2013
Externally published	Yes

Keywords

KdV equation
Soliton
Turbulence

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10.1016/j.physleta.2012.11.037

2-Soliton_turbulence-PLA_revisionAccepted author manuscript, 161 KBLicence: CC BY-NC-ND

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title = "Two-soliton interaction as an elementary act of soliton turbulence in integrable systems",

abstract = "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.",

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T1 - Two-soliton interaction as an elementary act of soliton turbulence in integrable systems

AU - Pelinovsky, E. N.

AU - Shurgalina, E. G.

AU - Sergeeva, A. V.

AU - Talipova, T. G.

AU - El, G. A.

AU - Grimshaw, R. H.J.

PY - 2013/1/3

Y1 - 2013/1/3

N2 - 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.

AB - 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.

KW - KdV equation

KW - Soliton

KW - Turbulence

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DO - 10.1016/j.physleta.2012.11.037

M3 - Article

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JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 3-4

ER -

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

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