The results of analytical and numerical investigations on the properties of
one-dimensional (nondrifting) solitons of relativistic amplitude, in the p
resence of an externally imposed uniform magnetic field B-0, are presented
and compared with those of the unmagnetized plasma theory (Esirkepov et al.
, Pis'ma Zh. Eksp. Teor. Fiz. 68, 33 (1998) [JETP Lett. 68, 36 (1998)]). Th
e presence of a uniform longitudinal magnetic field, the intensity of which
corresponds to an electron cyclotron frequency Omega(e) = eB(0)/m(e)c that
is a non-negligible fraction of the laser frequency Omega(0), has importan
t consequences on the properties of relativistically intense solitons. The
region of the parameter space (omega(0),Omega(e)) where magnetized solitons
exist is determined analytically, and new conditions of breaking due to th
e total density depletion are given. It is shown that stable high energy ma
gnetized solitons can be produced.