Other
Scientific paper
Jan 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992georl..19..143r&link_type=abstract
Geophysical Research Letters (ISSN 0094-8276), vol. 19, Jan. 24, 1992, p. 143-145; Authors' Reply, p. 147.
Other
Ion Acoustic Waves, Linear Evolution Equations, Magnetohydrodynamic Stability, Plasma Radiation, Wave Dispersion, Fourier Transformation, Green'S Functions, Laplace Transformation, Partial Differential Equations
Scientific paper
The paper puts into question the tenability of a critique by Oscarsson and Roennmark (1986) regarding the theory of absolute and convective instabilities. The space-time evolution of instabilities is reviewed with attention given to the two categories of time-asymptotic evolution. It is mentioned that the notion of time-asymptotics does not simply refer to t approaching infinity and that the evolution of the arbitrary initial perturbation at t = 0 is obtained by convolving the Green's function. The examples used in the previous critique describe instabilities that evolve in time only and are concluded to be nongeneric for continuous media, and the corresponding treatment of a time-asymptotic limit is characterized by imprecision. The original authors respond by suggesting that nondispersive waves are physically legitimate as in common plasma-wave modes and Alfven waves and can be described by their dispersion relation. A dispersive term is added to the relation so that it can be applied to ion-acoustic waves and other phenomena.
Bers Abraham
Ram Abhay K.
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