Nonlinear Alfven Wave in an Ultra-Relativistic Electron-Positron Plasma

Abstract

Nonlinear Alfven wave propagating parallel to a constant magnetic field in an ultra-relativistic electron-positron plasma is investigated in a frame of covariant two-fluid model equation. It is shown that the nonlinear evolution of circular polarized Alfven wave is described by \(\frac{\partial B}{\partial\tau}+a\frac{\partial^{3}B}{\partial\xi^{3}}+bB\frac{\partial}{\partial\xi}|B|^{2}+c|B|^{2}\frac{\partial B}{\partial\xi}=0,\) where B is the wave amplitude. Some stationary solutions (bright soliton, kink solution, spiky soliton with rapid phase rotation) are discussed.