Three-Soliton Interaction and Soliton Turbulence in Superthermal Dusty Plasmas

Abstract

Abstract Propagation and interaction of three solitons are studied within the framework of the Korteweg-de Vries (KdV) equation. The KdV equation is derived from an unmagnetised, collision-less dusty plasma containing cold inertial ions, stationary dusts with negative charge, and non-inertial kappa-distributed electrons, using the reductive perturbation technique (RPT). Adopting Hirota’s bilinear method, the three-soliton solution of the KdV equation is obtained and, as an elementary act of soliton turbulence, a study on the soliton interaction is presented. The concavity of the resulting pulse is studied at the strongest interaction point of three solitons. At the time of soliton interaction, the first- and second-order moments as well as the skewness and kurtosis of the wave field are calculated. The skewness and kurtosis decrease as a result of soliton interaction, whereas the first- and second-order moments remain invariant. Also, it is observed that the spectral index κ and the unperturbed dust-to-ion ratio μ have great influence on the skewness and kurtosis of the wave field.