The Riemann problem method for solving a perturbed nonlinear Schrodinger equation describing pulse propagation in optic fibres

Abstract

We used the Riemann problem method with a 3*3 matrix system to find the femtosecond single soliton solution for a perturbed nonlinear Schrodinger equation which describes bright ultrashort pulse propagation in properly tailored monomode optical fibres. Compared with the Gel'fand-Levitan-Marchenko approach, the major advantage of the Riemann problem method is that it provides the general single soliton solution in a simple and compact form. Unlike the standard nonlinear Schrodinger equation, here the single soliton solution exhibits periodic evolution patterns.