A nonlinear equation is derived and its analytic solution describing a soli
ton-like perturbation propagating at velocity close to the speed of light i
s found. It is shown that the rate at which the amplitude of a soliton exci
ted by a cold electron beam in a magnetized plasma-filled waveguide grows i
s proportional to (n(b)/n(0))(1/3), as is the linear growth rate of the bea
m-plasma instability. (C) 2000 MAIK "Nauka/Interperiodica".