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

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