KdV dynamics in the plasma-sheath transition

A mathematical model is formulated to catch the dynamics hidden in the plasma-sheath transition layer and the inner sheath layer for planar motion of a plasma. It is shown that the rescaled potential in the plasma-sheath transition layer and inner layer is governed by a perturbed KdV equation, through which some of the complex interactions and couplings among physical mechanisms acting in the plasma-sheath formation process are elucidated. This model is analyzed and compared with the model used by Fokas in his study of nonlinear dispersive initial boundary value problems [1].