On self-consistent stationary propagation of relativistically coupled electromagnetic and electrostatic waves in cold electron-ion plasma

A general self-consistent theory is presented for one-dimensional stationary propagation of relativistically coupled electromagnetic and electrostatic waves. A finite amplitude plane wave solution is found to be always unstable against modulation. A modulated finite amplitude plane wave solution is found in a narrow region of the frequency, and the possibility for a solitary wave solution and its properties are discussed.