Are weak dust-acoustic double layers adequately described by modified Korteweg–de Vries equations?

Abstract

Nonlinear double layers are investigated in dusty plasmas. The dust dynamics is modelled by a highly negatively charged and massive fluid in the presence of two isothermal proton populations. For electrostatic double layers one either integrates the cold dust equations exactly, to get a description in terms of a Sagdeev potential, or one uses a reductive perturbation analysis leading to modified Korteweg–de Vries equations. It is then shown that when the exact Sagdeev potential yields weak double layers, they can be quite different from what one would obtain via more approximate methods, and vice versa. This casts serious doubts upon the adequacy of modified Korteweg–de Vries equations for the description of weak double layers in more complicated cases where no exact analytical results are available. Such findings are relevant for different kinds of astrophysical and heliospheric plasmas, as well as for ordinary ion-acoustic double layers.