Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuations and statistics of solitonlike random pulses in a depleted pump

A phase quasi-integral for stimulated Raman scattering (SRS) is found. The relative phase of laser, Stokes, and polarization waves is found to be nearly conserved during their propagation in Raman media. Due to this quasi-integral, the temporal statistics of solitonlike pulses in a depleted pump is defined by phase statistics in the linear stage of SRS.