  The propagation of light beams in photovoltaic pyroelectric photorefractive
crystals is modelled by a specific generalization of the nonlinear
Schr\"odinger equation (GNLSE). We use the variational approximation (VA) to
predict the propagation of solitary-wave inputs in the crystal, finding that
the VA equations involve the dilogarithm special function. The VA predicts that
solitons and breathers exist, and the Vakhitov-Kolokolov criterion predicts
that the solitons are stable solutions. Direct simulations of the underlying
GNLSE corroborates the existence of such stable modes. The numerical solutions
produce both regular breathers and ones featuring beats (long-period
modulations of fast oscillations). In the latter case, the Fourier transform of
amplitude oscillations reveals a nearly discrete spectrum characterizing the
beats dynamics. Numerical solutions of another type demonstrate spontaneous
splitting of the input pulse in two or several secondary ones.
