  A case of moving one-dimensional electromagnetic (EM) solitons formed in a
relativistic interaction of a linearly polarized laser light with underdense
cold plasma is investigated. The relativistic Lorentz force in an intense laser
light pushes electrons into longitudinal motion generating coupled
longitudal-transverse wave modes. In a weakly relativistic approximation these
modes are well described by a dynamical equation of the generalized nonlinear
Schrodinger type, with two additional nonlocal terms [1]. An original
analytical solution for a moving EM soliton case is here calculated in an
implicit form. The soliton motion down-shifts the soliton eigen-frequency while
decreases its amplitude. An influence of the soliton velocity on stability
properties is analytically predicted.
