KDV Soliton Gas: Interactions and Turbulence

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.