On the solitonic structures of the cylindrical dust-acoustic and dust-ion-acoustic waves with symbolic computation

Dusty plasmas can support the dust-ion-acoustic and dust-acoustic modes, modelled by the cylindrical Korteweg-de Vries equation as proposed. In this Letter, we point out that there exist a couple of problems in the plasma-physics literature on the cylindrical Korteweg-de Vries equation, i.e., the claim of non-existence of exact analytic solutions and omission of varying ambient field, to which we provide our answers. With symbolic computation, we obtain a family of exact analytic, solitonic solutions, of which the previous solutions in plasma physics turn out to be the special cases. With figures, we work out some possibly observable effects for the future plasma experiments, featured by a solitonic pulse aboard the varying ambient field propagating with its varying velocity and amplitude.