Weak Ion-Acoustic Shock Waves

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Weak nonlinear ion-acoustic waves in a plasma consisting of cold ions and warm electrons are investigated by using a nonlinear perturbation method. In the lowest order of perturbation, it is found that the system of equations for the ion-acoustic waves can be reduced to the following single nonlinear dispersive-dissipative equation:<BR>(Remark: Graphics omitted.)<BR>where u, ξ and τ are normalized velocity of ion-fluid, stretched space and time coordinates, respectively. The parameter μ is a measure of dispersion due to charge separation, whereas ν is a measure of dissipation due to electron-ion collisions. It is shown that this equation has either oscillatory (dispersion-dominant case) or quasi-monotone (dissipation-dominant case) shock wave solutions.

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