  We investigate the interplay of diffraction and nonlinear effects during
propagation of very short light pulses. Adapting the factorization approach to
the problem at hand by keeping the transverse-derivative terms apart from the
residual nonlinear contributions we derive an unidirectional propagation
equation valid for weak dispersion and reducing to the
slowly-evolving-wave-approximation for the case of paraxial rays. Comparison of
numerical simulation results for the two equations shows pronounced differences
when self-focusing plays important role. We devote special attention to
modelling propagation of ultrashort terahertz pulses taking into account
diffraction as well as Kerr type and second order nonlinearities. Comparing
measured and simulated wave forms we deduce the value of the nonlinear
refractive index of lithium niobate in the terahertz region to be three orders
of magnitude larger than in the visible.
