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Abstract
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In this paper, we investigate the modulational instability and the possibility of electrostatic roguewave propagations in a completely degenerate plasma with arbitrary degree of degeneracy, i.e., relativistically degenerate plasma, ranging from solid density to the astrophysical compact stars. The
hydrodynamic approach along with the perturbation method is used to reduce the governing equations to the nonlinear Schr€odinger equation from which the modulational instability, the growth
rate of envelope excitations and the occurrence of rogue as well as super-rogue waves in the
plasma, is evaluated. It is observed that the modulational instability in a fully degenerate plasma
can be quite sensitive to the plasma number-density and the wavenumber of envelop excitations. It
is further revealed that the relativistically degeneracy plasmas (R0 > 1) are almost always modulationally unstable. It is found, however, that the highly energetic sharply localized electrostatic
rogue as well as super-rogue waves can exist in the astrophysical compact objects like white dwarfs
and neutron star crusts. The later may provide a link to understand many physical processes in such
stars and it may lead us to the origin of the random-localized intense short gamma-ray bursts,
which “appear from nowhere and disappear without a trace” quite similar to oceanic rogue
structures.
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