An investigation of acceleration waves in a perfectly conducting magnetohydrodynamic fluid (Q1117119)

This paper discusses the propagation of discontinuities in a perfectly conducting magnetohydrodynamic fluid, the model having been proposed by \textit{P. H. Roberts} [Q. J. Mech. Appl. Math. 34, 327-343 (1981; Zbl 0484.76126)] in the context of neutron stars. Roberts obtained a stability criterion which was subsequently reproduced by \textit{B. Straughan} [Z. Angew. Math. Phys 37, 274-279 (1986; Zbl 0597.76115)] using a discontinuity analysis but in the process the resulting sixth order secular equation decomposed into a product of quadratic and quartic polynomial factors. The first section of this paper investigates the reason for this factorization and the latter sections examine the nature of the equations governing the behaviour of the discontinuity amplitudes. The presence of the magnetic field effectively makes the fluid non- isotropic and so the determination of amplitude equations is non standard although they finally prove to be of Bernoulli type.