We examine the degenerate characteristics of the weakly ionized neutron stars (WINSs), while considering magnetic field quantization. A new set of quantum (QMHD) equations is obtained, which describes the homogeneous, weakly ionized, collisional degenerate neutron star. Then, using the obtained QMHD model, we have shown that in a WINS, electrons are responsible for the appearance of an additional term in momentum equations of neutrons, and hence, we formulate the linear dispersive properties of the medium. It is found that the nonlinear dispersive effects cause the broadening of the wave profile to balance the nonlinear steepening, so that the nonlinear stationary waves can be formed in the dispersive neutrino stars. In this context, it is demonstrated that neutron sound waves of WINS are described by two different modified Korteweg-de Vries equations. The present astrophysical plasma is highly recommended to investigate the propagation of proper waves in a strongly magnetized, ionized hydrogen atom.
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