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Considering the spatial distribution of laser beams and phonon waves, the SRS coupling wave equations in the transient regime are derived and normalized for the first time. The synchronously pumped solid-state Raman laser is simulated numerically to investigate the influences of the cavity length detuning, output coupling rate, dispersion, Raman gain and dephasing time of Raman mode on laser performances. It is found that the intensive pulse compression of first Stokes laser in synchronously pumped solid-state Raman laser stems from pulse width ga