The dielectric properties of Maxwellian plasmas are approximated using both Padé approximants to the dispersion function and direct approximation of the distribution. Physical constraints on permissible approximations are discussed, and it is found that some previously published results can lead to predictions of qualitatively incorrect wave properties, including unphysical negative damping. Approximate dispersion functions for Maxwellian distributions are given explicitly, and some of the effects of these approximations on the resulting dispersion are discussed. The approximations discussed here are of use both in analytic work and in accelerating large-scale numerical computations.

The nonlinear dynamics of a low-frequency electrostatic dissipative inhomogeneous plasma in an external magnetic field is studied for conditions above the critical point. The diffusion flux and the saturation level are self-consistently calculated from first principles, i.e. from the Braginskii equation.

Despite extensive theoretical investigation of the problem of ion-acoustic solitary waves in an inhomogeneous plasma, a fully satisfactory account has so far not been given. This paper provides a critical account of the shortcomings of the previous theoretical approaches and then describes a fully self-consistent treatment of the problem.

From the analysis of the symmetries of the derivative nonlinear Schrödinger (DNLS) equation, we obtain a new constant of motion, which may be formally considered as a charge and which is related to the helicity of the physical System. From comparison of these symmetries and those of the soliton solutions, we draw conclusions about the number of constraints that must be imposed and the way a Liapunov functional must be constructed in order to study the solitons' stability. We also examine the relationship between the stability with respect to form and the symmetries that are broken by the soliton solutions. We complete the analysis with some numerical simulations: we solve the DNLS equation taking a slightly perturbed soliton as an initial condition and study its temporal evolution, finding that, as expected, they are stable with respect to form.

A minor correction, having no major influence on our results, is reported here. The coefficients in the equations of state (16) and (17) should read

The set of equations (13)–(20) now comprise the correct, linearized and Fourierdecomposed double adiabatic equations in cylindrical geometry. In addition, there is a printing error in (15): a factor bz should multiply the last term of the left-hand side. Our results are only slightly modified, and the discussion remains unchanged. We wish, however, to point out that the correct stability criterion for isotropic pressure, (26), should be

This is the double adiabatic counterpart to the m ╪ 0 Kadomtsev criterion of ideal MHD.