Two-soliton interaction as an elementary act of soliton turbulence in integrable systems |
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| Authors: | EN Pelinovsky EG Shurgalina AV Sergeeva TG Talipova GA El RHJ Grimshaw |
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| Institution: | 1. Department of Information Systems, National Research University – Higher School of Economics, Nizhny Novgorod, Russia;2. Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia;3. Department of Applied Mathematics, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia;4. Department of Mathematical Sciences, Loughborough University, UK |
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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. |
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