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By assuming well defined magnetic surfaces we examine the characteristics of special three dimensional equilibria with incompressible flows such that any two out of the vectors of velocity, vorticity, magnetic field and current density are parallel one another. In the majority of the equilibria considered, it turns out that the only isodynamic equilibrium configuration, defined so that the magnetic field modulus be uniform on magnetic surfaces, is the axisymmetric Palumbo one. Also, except for equilibria with the velocity parallel to the current density in the other five of the above mentioned special axisymmetric (non-isodynamic) equilibria the velocity should be parallel to the magnetic field. In addition, isodynamicity is removed by the non parallel component of the flow associated with the electric field in axisymmetric equilibria with either complex lamellar generalised velocity, ρ V where ρ is the density, or complex lamellar magnetic field. [ABSTRACT FROM AUTHOR]

Magnetosonic waves traveling in a MHD equilibrium may evolve into shocks. We develop a criterion for the creation of fast shocks in the equatorial plane of axisymmetric equilibria and analyze the influence of the most important parameters. The results are applied to Grad–Shafranov equilibria and accretion disks. [ABSTRACT FROM AUTHOR]

Nonlinear waves advancing into equilibrium states may become shocks. This possibility depends on the equilibrium quantities plus the velocity and shape of the wavefronts. The equation describing this phenomenon is described for the case of the fast magnetosonic waves, and the particular case of plane flow with vertical magnetic field is analyzed in detail. It is also shown that in two-species MHD, both collisions between species and their chemical reactivity tend to delay or prevent the formation of shocks. [ABSTRACT FROM AUTHOR]

The equations of ideal magnetohydrodynamic equilibria in the presence of gravitational forcing and in the absence of pressure gradient are relevant for large-scale, extremely cold plasmas. Its 2D formulation possesses a highly symmetrical form that allows a complete analysis of its solvability. It turns out that when the boundary condition is given by the vanishing of the normal component of the magnetic field, in the absence of vacuum, solutions exist precisely for doubly connected domains, and in that case there exists an infinity of solutions. [ABSTRACT FROM PUBLISHER]

Formula (60) of the original paper yielding the curvature of the wavefront transported by straight rays is wrong. The correct one yields much more information on shock formation for the example developed in Section 4. [ABSTRACT FROM AUTHOR]