Motion invariants for a charge in a linearly polarized wave field

Six motion integrals for a relativistic charge in the field of a transverse linearly polarized electromagnetic wave propagating with an arbitrary phase velocity u>c were obtained by solving the canonical equations of motion. On the basis of these integrals, the charge trajectory as a function of the wave phase is analyzed in a fixed coordinate system. The coordinates, time, and phase are related by elliptic functions.