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A variable-coefficient unstable nonlinear Schrodinger model is hereby investigated, which arises in such applications as the electron-beam plasma waves and Rayleigh–Taylor instability in nonuniform plasmas. With computerized symbolic computation, families of exact analytic dark- and bright-soliton-like solutions are found, of which some previously published solutions turn out to be the special cases. Similarity solutions also come out, which are expressible in terms of the elliptic functions and the second Painleve transcendent. Some observable effects caused by the variable coefficient are predicted, which may be detected in the future with the relevant space or laboratory plasma experiments with nonuniform background existing.

Some recent observations of the ion-acoustic shocks in dusty plasmas have been explained via the one-dimensional Korteweg–de Vries–Burgers equation (1-D-KdVB). To help study the space and laboratory plasma systems, the investigation on a two-dimensional generalization of the 1-D-KdVB is performed with computerized symbolic computation. An auto-Backlund transformation and some monotonic-shock-wave-like, exact analytic solutions are found. Then, several observable effects are predicted, which the future space and laboratory plasma experiments might discover, beyond the existing one-dimensional and traveling-wave considerations.

The variable-coefficient unstable nonlinear Schrodinger equation describes the nonlinear modulation of the high-frequency mode in the electron beam plasma, with a nonuniform background. In this paper, an auto-Backlund transformation and several families of the exact analytical solutions to the variable-coefficient unstable nonlinear Schrodinger equation are presented. One family turns out to be soliton-typed.

The dust ion-acoustic shocks in an unmagnetized dusty plasma have recently been observed, and their dynamics have been shown to be governed by a Korteweg–de Vries–Burgers (KdVB) equation, which is briefly mentioned to admit both oscillatory and monotonic shocks [Phys. Plasmas 7, 1044 (2000)]. However, we point out that the analytic expressions are a must to help us to a better understanding of the plasma system under investigation, but the aforementioned paper does not provide us with such information for the dust ion-acoustic shocks. To make the story complete, we hereby present some exact and approximate analytic solutions to the KdVB equation along with the original papers, which agree well with the recent observations.

In a cosmic dusty plasma, both azimuthal and height perturbations of a nonplanar cylindrical geometry are considered. For dust-ion-acoustic waves and with symbolic computation, (3+1)-dimensional generalized Johnson [(3+1)DGJ] model is derived and analytic solutions are constructed. Supernova-shell-typed expanding bright (3+1)DGJ nebulons and Saturn-F-ring-type expanding dark (3+1)DGJ nebulons are both pictured and discussed. Essential difference of this letter from the existing literature is pointed out, with the relevant, possibly observable (3+1)DGJ-nebulonic structures for the future cosmic experiments proposed.

The spherical modified Kadomtsev-Petviashvili (smKP) model is hereby derived with symbolic computation for the dust-ion-acoustic waves with zenith-angle perturbation in a cosmic dusty plasma. Formation and properties of both dark and bright smKP nebulons are obtained and discussed. The relevance of those smKP nebulons to the supernova shells and Saturn’s F-ring is pointed out, and possibly observable nebulonic effects for the future cosmic plasma experiments are proposed. The difference of the smKP nebulons from other types of nebulons is also analyzed.

In a cosmic dusty plasma, the dust-acoustic-wave propagation may be described by a cylindrical Kadomtsev-Petviashvili equation. In this Letter, for such modeling of environments like supernova shells, Saturn’s F-ring, etc., cylindrical nebulons and an auto-Backlund transformation are presented via symbolic computation. Nebulon structures are discussed, and possibly observable effects are proposed for cosmic plasmas.

Dusty plasmas have been found almost everywhere in the Universe. Sahu and Roychoudhury [Phys. Plasmas 10, 4162 (2003)] have done their interesting analytic work on the cylindrical dust ion-acoustic waves, without enough guidance to the readers on other existing analytic results. Such lack of guidance turns out to be critical. We hereby try to make the story more complete in the sense that the model does have plenty of exact analytic solutions published already, and to present a brief review on some of them. For the dust-ion-acoustic and dust-acoustic modes supported by the space/laboratory dusty plasmas, we hereby picture out some possibly observable effects for the future experiments, featured by a solitonic pulse aboard the varying ambient field propagating with its varying velocity and amplitude.