Damping Solitary Wave in a Three-Dimensional Rectangular Geometry Plasma

The solitary waves of a viscous plasma confined in a cuboid under the three types of boundary condition are theoretically investigated in the present paper. By introducing a three-dimensional rectangular geometry and employing the reductive perturbation theory, a quasi-KdV equation is derived in the viscous plasma and a damping solitary wave is obtained. It is found that the damping rate increases as the viscosity coefficient increases, or increases as the length and width of the rectangle decrease, for all kinds of boundary condition. Nevertheless, the magnitude of the damping rate is dominated by the types of boundary condition. We thus observe the existence of a damping solitary wave from the fact that its amplitude disappears rapidly for a →0 and b→0, or ν'→+∞.