  The bright soliton in optical fiber is generally investigated via its spatial
evolution in the time domain, where its waveform is considered in many studies.
To be consistent with the well-established picture of the dynamics of solitons
in other systems, in this letter, we propose it is helpful to study the
temporal evolution of the bright soliton by examining its waveshape propagating
along the space coordinate axis. We develop a singular theory. Equations
governing the evolution of the parameters of the bright soliton in the slow
time and the radiated field are explicitly formulated for the first time. In
addition, localized modes are found to appear.
