Time-fractional Boussinesq equation for heavy-nucleus-acoustic wave excitations in highly dense relativistically degenerate quantum plasmas

Abstract

The dynamics of nonlinear propagation of the heavy-nucleus-acoustic waves (HNAW) is theoretically investigated in a plasma comprising non-degenerate inertial heavy ions, degenerate non-relativistic non-inertial light ions, and degenerate electrons-positrons with relativistic velocity. At first, the classical Boussinesq equation is obtained, then using Agrawal’s method, it is transformed into the time-fractional Boussinesq equation to observe the effects of time-fractional parameter on the propagation dynamics of HNAW, where the notion of the Riesz fractional derivative refers to the time-fractional term. The variational iteration method is employed to construct the heavy-nucleus-acoustic solitary wave solution which later turns into an oscillatory wave pulse. It comes out that the heavy-nucleus acoustic waves’ amplitude is greatly altered by the time-fractional parameter. We have briefly explored the impact of plasma parameters on the creation and propagation of heavy-nucleus acoustic waves. The significance of our findings is emphasized in relation to the highly dense relativistic astrophysical plasmas usually observed in dense stars.