Dust acoustic solitons in a dusty plasma with Cairns–Gurevich distributed ions

The problem of dust acoustic solitons is addressed in an unmagnetized collisionless dusty plasma with ions satisfying a Cairns–Gurevich distribution. A new type of density that describes, simultaneously, the evolution of the energetic ions and those trapped in the plasma potential well is outlined. Both highly and weakly nonlinear waves are investigated by deriving the Sagdeev potential for the large amplitude limit, and establishing the nonlinear partial differential equations (mK–dV equation) for the small but finite amplitude limit. It is shown that the effect of the nonthermal ion trapping on DA waves can be quite important. In particular, an increase of nonthermal character of ions following the Cairns–Gurevich distribution lead to an increase of the main quantities (amplitude and width) of dust acoustic solitons. Our investigation will be helpful in understanding the nonlinear DA waves in the presence of nonthermal trapped ions which may exist in space.