New exact analytical solutions describing the non-stationary propagati
on of non-sine electromagnetic waves in plasma are obtained by direct
solution of Maxwell equations without the traditional Fourier transfor
mations. Unlike the usual travelling monochromatic waves the fields di
scussed are distinguished by unequal periods of electric and magnetic
oscillations, fast oscillative diffusion of the envelope and collision
less damping of peak amplitudes due to strong plasma dispersion. The t
ransformation of these non-sine fields to the trains of quasimonochrom
atic waves in the depth of plasma is considered for both isotropic and
magnetized plasmas.