  We employ the Sagdeev pseudo-potential method to investigate the propagation
of nonlinear ion waves in a relativistically degenerate electron-ion plasmas.
The matching criteria for existence of such nonlinear excitations are
numerically investigated in terms of the relativity measure (relativistic
degeneracy parameter) of electrons and the allowed Mach-number range for
propagation of such waves is evaluated. It is shown that the electron
relativistic degeneracy parameter has significant effects on nonlinear wave
dynamics in superdense degenerate plasmas such as that encountered in white
dwarfs and the cores of massive planets.
