Exact localized nonlinear dust kinetic Alfvén waves are investigated by retaining the complete dust nonlinearity and by invoking small but finite-β effects in a collisionless plasma, whose constituents are electrons, ions and negatively charged dust grains. Sub-Alfvénic, as well as super-Alfvénic, solitary waves consisting of smooth density humps or dips are found to exist. Further, super-Alfvénic kink type solitons are also found to occur. The soliton amplitude depends upon various plasma parameters along with the soliton propagation speed. The results of the present investigation may be useful in the diagnostics of dust in magnetized plasmas and in understanding the formation of coherent soliton structures in space and laboratory plasmas.

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A numerical study of a one-dimensional collisionless ion-acoustic shock generated by an injection of a plasma beam is presented. The electrons are assumed to be hot and isothermal, and obey the Boltzmann distribution; the ions are described by the Vlasov equation which is solved by a direct finite difference scheme. There is a threshold beam velocity ubm, above which shock is not generated. ubm is a function of the beam-background density ratio and the electron-ion temperature ratio, and is larger than the limit of the ion-ion two-stream instability uts. For beam velocities ranging from zero to uts a shock is observed followed by a region of fully developed two-stream instability. For beam velocities between uts and ubm, a shock and a phase-space vortex are formed and in between them a quiescent region grows. A stable two-stream remains behind the vortex.