Kadomtsev-petviashivili equation for the relativistic electromagnetic soliton in the collisionless electron-positron-ion plasma

With an externally applied uniform magnetic field, a Kadomtsev-Petviashivili (KP) equation is derived to study the perpendicular nonlinear wave in a collisionless plasma consisting electrons, positrons, and ions for weak relativistic limit. The stationary solution was presented for the group velocity, amplitude, and width of the soliton. It is shown that both the externally imposed magnetic field and the ratio of the ion equilibrium density to the electron equilibrium density influence strongly the group velocity, amplitude, and width of the KP soliton. By using the figure analysis, we study the interaction law of the two parallel line-solitons.