Аннотация:Novel effects for few-cycle pulses propagation in quadratic media with dispersion management are considered. First, the process of extraordinary wave generation in uniaxial crystal is tightly related with the process of ordinary wave profile differentiation. Velocity mismatch limits interaction efficiency and leads to splitting of generated waves into two subpulses. Such effect can be suppressed in the medium with periodic modulation of quadratic nonlinearity or with velocity mismatch sign modulation. Second, highly interesting effects arise with the third-order dispersion. Dispersive spreading can be reduced in layered medium with alternating third-order dispersion coefficients. Quadratic photonic crystals with modulated dispersion coefficients or with managed dispersion are very promising for few-cycle pulse nonlinear optics. One- and two-wave soliton trapping and propagation dynamics are also studied in such crystals. The analytical theory is accompanied with the numerical simulation results.