Abstract
By using the hydrodynamic equations of positive and negative ions, the Boltzmann electron density distribution and the Poisson equation with stationary dust, a three-dimensional (3D) Zakharov-Kuznetsov (ZK) equation is derived for small but finite amplitude ion-acoustic waves. However, the ZK equation is not appropriate to describe the system either at critical plasma compositions or in the vicinity of the critical plasma compositions. Therefore, the modified ZK (MZK) and extended ZK (EZK) equations are derived. The generalized expansion method is used to analytically solve the ZK, MZK and EZK equations. A new class of solutions that admits a train of well-separated bell-shaped periodic pulses is obtained. In certain conditions, the latter degenerates to either solitary or shock wave solutions. The effects of the physical parameters on the nonlinear structures are examined in many plasma environments having different negative ion species, such as D- and F-regions of the Earth's ionosphere, as well as in laboratory plasma experiments. Numerical analysis of the solutions revealed that the profile of the nonlinear pulses suffers amplitude and width modifications due to enhancement of the dust practices, negative ions, positive-to-negative ion mass ratio and positive/negative ion cyclotron frequency. Furthermore, the necessary conditions for both solitons and shocks propagation as well as their polarity are examined.