Relativistic degenerate effects of electrons and positrons on modulational instability of quantum ion acoustic waves in dense plasmas with two polarity ions

The nonlinear propagation of quantum ion acoustic wave (QIAW) is investigated in a four-component plasma composed of warm classical positive ions and negative ions, as well as inertialess relativistically degenerate electrons and positrons. A nonlinear Schrödinger equation is derived by using the reductive perturbation method, which governs the dynamics of QIAW packets. The modulation instability analysis of QIAWs is considered based on the typical parameters of the white dwarf. The results exhibit that both in the weakly relativistic limit and in the ultrarelativistic limit, the modulational instability regions are sensitively dependent on the ratios of temperature and number density of negative ions to those of positive ions respectively, and on the relativistically degenerate effect as well.