A Korteweg–de Vries Burgers-like equation for weakly nonlinear dust ion-acoustic waves in a charge-varying dusty plasma with nonthermal electrons

A weakly nonlinear analysis is carried out to derive a Korteweg–de Vries Burgers-like equation for small but finite amplitude dust ion-acoustic (DIA) waves in a charge varying dusty plasma with non thermally distributed electrons. The correct expression for the nonthermal electron charging current is used. Interestingly, it may be noted that due to electron nonthermality and finite equilibrium ion streaming velocity, the present dusty plasma model can admit compressive as well as rarefactive DIA solitary waves. Furthermore, there may exist DIA shocks which have either monotonic or oscillatory behavior and the properties of which depend sensitively on the number of fast nonthermal electrons. Our results should be useful to understand the properties of localized DIA waves that may occur in space dusty plasmas.