KDV Soliton Gas: Interactions and Turbulence

Part of the Nonlinear Systems and Complexity book series (NSCH, volume 20)


The collective behavior of soliton ensemble corresponded to soliton turbulence is studied within the integrable Korteweg–de Vries (KdV) equation. Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. The amplitude of the resulted impulse decreases during the nonlinear interaction. It leads to the changing of characteristics of whole multi-soliton field. Numerical simulation of soliton ensemble within the KdV equation is performed. Statistical moments of wave fields and distribution functions of wave amplitudes are found and analyzed. Skewness and kurtosis decrease due to soliton interaction. The criterion of “small” soliton’s negative velocity in soliton gas is obtained.


Korteweg-de Vries equation Solitons Ensemble Statistics 



Different parts of the study were funded by RFBR (16-02-00167, 16-05-00049, 16-35-00175). The study of the effect of a negative soliton velocity was particularly funded by RFBR (16-32-60012). The authors also gratefully acknowledge the support from Volkswagen Foundation and President grant SC-6637.2016.5.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Applied PhysicsNizhny NovgorodRussia
  2. 2.Nizhny Novgorod State Technical UniversityNizhny NovgorodRussia
  3. 3.National Research University – Higher School of EconomicsNizhny NovgorodRussia

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