Dust-ion-acoustic envelopes and modulational instability with relativistic degenerate electrons

Amplitude modulated unstable nonlinear structures have been studied in a three component dusty plasma consisting of degenerate relativistic electrons, degenerate ions, and negatively charged static dust grains. Following the multiscale reductive perturbation method, a nonlinear Schrödinger equation is derived, which not only admits the modulational instability but also causes the evolution of unstable excitations, namely, bright solitons and rogons. Numerical analysis illustrates that modulationally unstable wave envelopes are obtained in the limit of long wave number for taking cold and nondegenerate ions (the ratio of ion Fermi-to-electron rest mass energy, g = 0); however, the ionic Fermi pressure leads to stable excitations. It is observed that modulationally unstable wave packets are excited even for ultra small wave number (k≪1) when the dust concentration parameter exists in the range μc1<μ<μc2, where μc1 and μc2 being the critical values. Furthermore, it is revealed that these critical values are quite sensitive to the variation of electron relativistic degeneracy (ηe0) and the carrier wave number. The present results elucidate the important features of localized dust-ion-acoustic excitations due to self interactions in superdense astrophysical plasmas, viz., white dwarf, neutron stars, etc.