This paper applies three-wave interaction (TWI)-soliton theory to optical p
arametric amplification when the signal, idler, and pump wave can all conta
in TWI solitons. We use an analogy between two different velocity regimes t
o compare the theory with output from an experimental synchronously pumped
optical parametric amplifier. The theory explains the observed inability to
compress the intermediate group-velocity wave and 20-fold pulse compressio
n in this experiment. The theory and supporting numerics show that one can
effectively control the shape and energy of the optical pulses by shifting
the TWI solitons in the pulses. [S1063-651X(99)16505-X].