Kadomtsev--Petviashivili equation for an ion-acoustic soliton in a collisionless weakly relativistic plasma with finite ion temperature

A Kadomtsev--Petviashivili equation is derived for a two-dimensional ion-acoustic soliton propagating in a collisionless weakly relativistic plasma containing the finite temperature ions. This equation is solved in a stationary frame to obtain expressions for the phase velocity, amplitude, width, peak ion density, peak pressure, and energy of the soliton. It is shown that both the relativistic effect and the ion temperature greatly influence the phase velocity, amplitude, and the width. The soliton behavior is described in detail, and a comparison is made between the present results and the previous theories