Stability and evolution of ion-acoustic solitons in strongly coupled relativistic degenerate pair plasmas

We have studied the nonlinear propagation of ion-acoustic waves (IAWs) in a collisionless magnetized plasma composed of strongly coupled pair of ions and relativistic degenerate inertia-less electrons and positrons. Starting from a generalized visco-elastic hydrodynamic model for both positive and negative ions and using the reductive perturbation technique, a (3 + 1)-dimensional Zakharov-Kuznetsov (ZK) equation is derived which governs the evolution of weakly nonlinear IAWs in a multi-component magneto-pair-plasma. It is found that the nonlinear wave speed is significantly modified by the magnetic field strength similar to magneto-acoustic waves and the relativistic degeneracy of electrons and positrons. A travelling wave solution of the ZK equation is obtained and its stability is studied. Different stable and unstable regions are obtained and analyzed. It is shown that the growth rate of instability is reduced by the effects of the degeneracy of electrons and positrons, and the obliqueness of propagating solitons in strongly coupled regimes. The results should be useful for understanding the existence and stability of ion-acoustic solitons in strongly coupled dense astrophysical objects.