The separation of one-soliton-shock to multi-soliton-shock of dust-ion acoustic wave using Lax pair and Darboux transformation of Burgers’ equation

Abstract

Properties of dust-ion acoustic waves (DIAWs) in an unmagnetized dusty plasma consisting of mobile ions, superthermal electrons, and negatively charged dust clouds with charge fluctuation are investigated. Burgers’ equation is derived from the fluid equation of the plasmas by considering the reductive perturbation technique. The Lax pair of the evolution equation is obtained, and the characteristics of the DIAWs are investigated by employing the Darboux transformation. Some new waves (one-soliton, two-soliton-shocks, etc.) other than usual shocks are observed as the Darboux transformation is used through the Lax pair. It is also shown that all the physical plasma parameters have a significant effect on the structure of the nonlinear waves.