[en] Highlights: • Interaction of the graphene quasiparticles with a slow-light pulse. • The Volkov's solution for graphene quasiparticles in the electromagnetic wave. • The Fock-Schwinger proper time method. • The Green's function for graphene quasiparticles in the electromagnetic wave. An analytical Volkov's solution of the massless Dirac equation for graphene in the field of slow-light pulse with arbitrary time dependence is obtained. Exact solutions are presented for special cases of monochromatic field and a single-cycle pulse. Following the Fock-Schwinger proper time method, the Green's function for quasiparticles is derived with the account of the influence an external classical electromagnetic wave field.