Abstract
Recent experimental observations of stimulated Raman scattering have observed an anomalous reversal of pump depletion under certain circumstances. This reversal of the pump depletion has been interpreted by Drühl, Carlsten, and Wenzel as a heavily-damped soliton whose width narrows as it propagates in the Raman-active medium. In this paper, I solve the initial value problem for such a system. Furthermore, I find that I can theoretically predict the number of such solitons which shall appear as well as give the conditions necessary for such solitons to occur. Lastly, by using the proper solution for the initial value problem, I can verify the correctness of the results given by Drühl, Carlsten, and Wenzel for the position and widths of such solitons.
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