  It has been established for some time that high-power pump can trap a probe
beam of lower intensity that is simultaneously propagating in a Kerr-type
optical medium, inducing a focusing of the probe with the emergence of modes
displaying solitonic properties. To understand the mechanism by which such
self-sustained modes are generated, and mainly the changes on probe spectrum
induced by the cross-phase-modulation effect for an harmonic probe trapped by a
multiplex of temporal pulses, a linear equation (for the probe) and a nonlinear
Schr\"odinger equation (for the pump) both coupled by a cross-phase-modulation
term, are considered simultaneously. In general the set of coupled probe-pump
equations is not exactly tractable at any arbitrary value of the ratio of the
cross-phase to the self-phase modulation strengths. However, for certain values
of this ratio, the probe modulation wavector develops into $|n,l\textgreater$
{\it quantum states} involving $2n+1$ soliton-shaped eigenfunctions which
spectral properties can be characterized unambiguously. Solutions of the probe
equation give evidence that the competition between the self-phase and
cross-phase modulations leads to a broadband spectrum, with the possibility of
a quasi-continuum of soliton modes when the cross-phase-modulation coupling is
strong enough.
