Abstract

Formation of the dense collection if solitons in the Raman scattering has been investigated by the several authors^[1-3] with using the inverse scattering transform under specific initial conditions. Study of the common case required another approach. Development of a new method of analysis of the densely packed short pulses based on the hydrodynamics descriptions for investigation of coherent Raman scattering and two-photon propagation is a goal of this work. One of onsets of the dense configuration of pulses may be the evolution of nondispersive shock waves in nonlinear medium. The dynamics simulation showed the common feature of such evolution–the shock waves are smoothed by the high frequency nonlinear waves. The second origine is decay of unstable initial state.^[1] The problem is solved in a few steps. Firstly the new common periodic solution of the evolution equations is found. The second step consists in averaging of integrals over the period of fast oscillations. This yields a set of hydrodynamical Whitham eqs. for slow changing parameters of the solution. The simplest one-phase solution has two independent parameters. Imposing the specified boundary condition makes the dressing of initial step like form of a shock wave by the smoothing oscillations. The new perturbation theory based on developed approach is used here for studying of the influence of relaxation, diffraction and nonlinear frequency shift. The perturbations make alteration of a form of envelope of a pulse train and inner dynamics of configuration. It is found that relaxation yields squeezing of the train. This result may be used for explanation of experimental data (see Ref. ¹). It is demonstrated that the form of an envelope is unstable with respect to long wave modulation. Thus the configuration of solitons changes its form with time. The theory presented here is used to find time and distance dependence of parameters related with a leading edge of a train and distance between pulses which are in agreement with experimental data.

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