Abstract
In the present work is being reviewed the evolution of one-dimensional femtosecond optical pulses with large spectral bandwidth in a single-mode fiber. The corresponding scalar nonlinear amplitude equation is used which describes the propagation of such pulses. It significantly differs from the ordinary Nonlinear Schrodinger equation. It appears that nonlinear term oscillates at a frequency proportional to the difference between the group and phase velocity of the pulse. This equation includes a term containing the first order of dispersion of the group velocity and the second derivatives of the coordinate z and the time t. It is assumed that the losses in the fiber are not significant and they will not be counted. An accurate analytical solution of this equation is found. It describes the evolution of soliton-like pulses in single-mode fiber. This soliton has different characteristics from those of the soliton obtained by solving the nonlinear Schrodinger equation.
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