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Temporal evolution of the bright soliton in an optical fiber

The bright soliton in an optical fiber is generally studied by treating the spatial variable as the evolution variable, where the waveform is taken into consideration. To be consistent with the well-established picture of the dynamics of solitons in other systems, in this letter, we propose that it is helpful to take the temporal variable as the evolution one and study the waveshape of the bright soliton via its propagation along the space coordinate axis. We develop a singular theory. Equations governing the evolution of parameters of the bright soliton in the slow time and the radiated field are explicitly formulated for the first time.