  Wave modes induced by cross-phase reshaping of a probe photon in the guiding
structure of a periodic train of temporal pulses are investigated theoretically
with emphasis on exact solutions to the wave equation for the probe. The study
has direct connection with recent advances on the issue of light control by
light, the focus being on the trapping of a low-power probe by a temporal
sequence of periodically matched high-power pulses of a dispersion-managed
optical fiber. The problem is formulated in terms of the nonlinear optical
fiber equation with averaged dispersion, coupled to a linear equation for the
probe including a cross-phase modulation term. Shape-preserving modes which are
robust against the dispersion are shown to be induced in the probe, they form a
family of mutually orthogonal solitons the characteristic features of which are
determined by the competition between the self-phase and cross-phase effects.
Considering a specific context of this competition, the theory predicts two
degenerate modes representing a train of bright signals and one mode which
describes a train of dark signals. When the walk-off between the pump and probe
is taken into consideration, these modes have finite-momentum envelopes and
none of them is totally transparent vis-\`a-vis the optical pump soliton.
