A detailed study of a system of coupled waves is given for which an initial-boundary value problem is solved by means of the spectral transform theory. This system represents the nonlinear interaction of an electrostatic high-frequency wave with the ion acoustic wave in a two component homogeneous plasma. As a result it is understood the plasma instability as (i) a continuous secular transfer of energy from the laser beam to the acoustic wave, (ii) the evolution toward the formation of local singularities of the electrostatic wave (collapsing), (iii) a mutual trapping of the acoustic wave and the scattered Langmuir wave.
By using the inverse spectral transform, the SRS equations are solved and the explicit output data is given for arbitrary laser pump and Stokes seed profiles injected on a vacuum of optical phonons. For long duration laser pulses, this solution is modified such as to take into account the damping rate of the optical phonon wave. This model is used to interprete the experiments of Drühl, Wenzel and Carlsten (Phys. Rev. Lett., (1983) 51, 1171), in particular the creation of a spike of (anomalous) pump radiation. The related nonlinear Fourier spectrum does not contain discrete eigenvalue, hence this Raman spike is not a soliton.
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