Abstract
We used the Riemann Problem Method with a 3 X 3 matrix system to find the single soliton solution for a perturbed nonlinear Schrodinger equation in the most compact form. The considered equation describes bright ultrashort pulse propagation in properly tailored monomode optical fibers. The propagation of different single soliton solutions under the influence of the self-induced Raman effect was illustrated. Unlike the single soliton solution of the standard nonlinear Schrodinger equation we found that one of the our soliton solution can exhibit instability which leads to soliton fission.
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