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We employ the Sagdeev pseudo-potential method to investigate the propagationof nonlinear ion waves in a relativistically degenerate electron-ion plasmas.The matching criteria for existence of such nonlinear excitations arenumerically investigated in terms of the relativity measure (relativisticdegeneracy parameter) of electrons and the allowed Mach-number range forpropagation of such waves is evaluated. It is shown that the electronrelativistic degeneracy parameter has significant effects on nonlinear wavedynamics in superdense degenerate plasmas such as that encountered in whitedwarfs and the cores of massive planets.

Propagation of arbitrary-amplitude ion waves in relativistically degenerate electron-ion plasmas