  We develop reduced models that describe half-harmonic generation in a
synchronously-pumped optical parametric oscillator above threshold, where
nonlinearity, dispersion, and group-velocity mismatch are all relevant. These
models are based on (1) an eigenmode expansion for low pump powers, (2) a
simulton-like sech-pulse ansatz for intermediate powers, and (3) dispersionless
box-shaped pulses for high powers. Analytic formulas for pulse compression,
degenerate vs. nondegenerate operation, and stability are derived and compared
to numerical and experimental results.
