Nonlinear solitons of modified Zakharov--Kuznetsov equation in an inhomogeneous collisional plasma

The Zakharov--Kuznetsov equation is a nonlinear wave equation that was first derived for a lossless magnetized plasma. In this paper, we investigate the nonlinear wave equation in an inhomogeneous magnetized plasma and the applications of the solitary wave solutions, considering the collision effect. The nonlinear wave propagation is studied by the two-dimensional modified Zakharov--Kuznetsov (mZK) equation, including the collision mechanism. By using the (G'/G)-expansion method, different forms of analytical solutions of the new mZK equation, such as solitons, trigonometric, hyperbolic and rational function solutions have been obtained. These solutions describe the perturbed electric field potential and/or electric field in the form of travelling solitary wave solutions. The proposed model equation explains how two-dimensional waves propagate in different physical conditions of the plasma. The wave propagation is analyzed by illustrating the spatial-temporal behavior of the exact solutions. Three types of motion can be observed for solitary waves, including single- and multi-period regimes for right-propagating soliton, and stochastic regimes for left-propagating soliton. The turbulent regime of stabilization, stochasticity, and modulation due to different electrostatic polarities contributes to ion acceleration. The co-existence of positive- and negative-polarized solitons confirms that the mZK equation is invariant for inversion of polarity.