Three-dimensional nonlinear ion acoustic waves near critical density in magnetized negative ion plasmas

Abstract

The nonlinear dynamics of three-dimensional ion acoustic waves near critical density in plasmas consisting of electrons, positive and negative ions in the presence of a uniform external magnetic field are investigated. In the weak nonlinear and dispersive limit, the nonlinear wave is shown to be governed by a Gardner–Zakharov–Kuznetsov (GZK) equation, which is also shown to be integrable in the sense of Painlevé only on the traveling wave frame. The invariant Painlevé analysis provides the analytical solutions in the closed form of solitary, cnoidal, double layer and bipolar structures. The Lyapunov stability analysis shows that the stationary solitary structure is always unstable due to the three-dimensional effect. Finally, the stability of one-dimensional solitary wave has been checked in the transverse direction and the regions of stability (and instability) have been separated in terms of parameters. The results are in qualitative agreement with the observations in magnetized plasmas with negative ions.