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We exactly solve the initial-boundary value problem of interaction of three waves in the limit when one of these waves is strongly damped. The solution is applied to the characterization of transient effects in Raman amplifiers, with a special emphasis on the possibility of generating Stokes pulses with peak powers that are orders of magnitude higher than the input power of the pump beam.

Exact solution for the gigantic amplification of ultrashort pulses in counterpumped Raman amplifiers