Two-evolution equations for nonlinear subpicosecond pulses in optical fibers and their equivalent solitary solutions

Abstract

Abstract By means of the multiscale singular perturbation method and directly from the Maxwell vector wave equation containing the nonlinear polarization term, we have obtained two kinds of equations describing the propagation of nonlinear sub-picosecond optical pulse in optical fibers. These two equations are the nonlinear Schrodinger equations with different linear combinations of the higher order terms (the higher order dispersion term, the self-steepening term, and the delayed nonlinear response term). The approximate coefficients of the equations are derived under the weakly guiding condition. Using a perturbation method, we show that these two equations share a solitary wave solution.