  Arbitrary amplitude nonlinear ion waves is investigated in an extremely
degenerate electron-positron-ion plasma with relativistic electrons/positrons
and dynamic cold ions using Sagdeev pseudo-potential method in framework of
quantum hydrodynamics model. The matching criteria of existence for ion
solitary as well as periodic nonlinear excitations is studied numerically in
terms of the relativistic degeneracy parameter, relative positron concentration
and the relativistic normalized propagation-speed range of these waves are
obtained. It is remarked that the electron relativistic degeneracy and relative
positron concentration in such plasmas have significant effects on nonlinear
wave propagations in relativistically degenerate Fermi-Dirac plasma. Our
results are in good agreement with the previously reported ones obtained using
semiclassical Thomas-Fermi approximation in dense plasmas with non-relativistic
and ultra-relativistic electrons and positrons. Current findings can be
appropriate for the study of astrophysical superdense compact objects such as
white dwarfs.
