Relativistic Electromagnetic Solitary Wave in a Cylindrical Magnetized Plasma

In the presence of an applied static and uniform magnetic field, a cylindrical Kadomtsev--Petviashivili equation is derived for a relativistic electromagnetic solitary wave propagating in collisionless plasma consisting electrons, positrons, and ions in the case of weak relativistic limit. This equation is solved in a stationary frame to obtain explicit expression for the velocity, amplitude and width of solitons. The amplitude of the solitary wave has a maximum value at a critical α_c of the ratio of the ion equilibrium density to the electron one, and it increases as the applied magnetic field becomes larger.