Abstract
The three-dimensional instability of isothermal ion-acoustic (IIA) solitary waves is examined in a magnetized ultra-relativistic degenerate multicomponent plasma, comprising nondegenerate inertial warm ions and ultra-relativistic degenerate inertialess electrons as well as positrons, by applying a small-k (long wavelength) expansion method. The nonlinear dynamics of IIA solitary waves in such a plasma model are governed by the nonlinear Zakharov-Kuznetsov equation. To perform the analysis, the instability criterion and the growth rate of the instability of IIA solitary waves have been obtained. A careful investigation shows that the amplitude, the width, the growth rate, and the instability of IIA solitary waves increase with the increasing chemical potential of electrons. The stable region of IIA solitary waves increases with the increasing fermion population and the angle between the directions of propagation and the uniform magnetic field. The present study may be helpful for elucidating the physical nature of nonlinear waves in compact objects such as white dwarfs and neutron stars where the concentration of degenerate ultra-relativistic electrons and positrons and their chemical potentials play a crucial role.