Cylindrical Kadomtsev–Petviashvili equation for relativistically magnetosonic solitary wave in the collisionless plasma

In the presence of an applied static and uniform magnetic field, a cylindrical Kadomtsev–Petviashvili (CKP) equation is derived for a relativistically magnetosonic solitary wave propagating in a collisionless plasma in the case of weak relativistic limit. The equation is solved in a stationary frame to obtain a particular solution. It is shown that the externally imposed magnetic field greatly influences the phase velocity, amplitude and width of the CKP soliton.