Asymptotically Stable Electromagnetic Shock Waves in Relativistic Plasmas

The behavior of electromagnetic (EM) waves in a relativistic plasma is investigated. The governing equations of such dynamical plasma system are derived from the basic fluid model equations, and the vector and electrostatic potential are analyzed using Maxwell’s equations. A system of first-order, ordinary but nonlinear differential equations, is obtained from the two coupled second-order differential equations. Numerical results are found using the fourth order Runge–Kutta method. It is seen that EM shock waves are emerged for subsonic case, and on the other hand, periodic oscillatory solution as well as asymptotically stable state is obtained for supersonic case. The present investigation is important to extrapolate in different plasma backgrounds, like laboratory and astroplasma environments, viz., in laboratory biomedicine, biophysics, genetic engineering, laboratory astrophysics, and at different stages of stellar evolution.