  A model is introduced to describe guided propagation of a linear or nonlinear
pulse which encounters a localized nonlinear defect, that may be either static
or breather-like one (the model with the static defect applies to an optical
pulse in a long fiber link with an inserted additional section of a nonlinear
fiber). In the case when the host waveguide is linear, the pulse has a Gaussian
shape. In that case, an immediate result of its interaction with the nonlinear
defect can be found in an exact analytical form, amounting to transformation of
the incoming Gaussian into an infinite array of overlapping Gaussian pulses.
Further evolution of the array in the linear host medium is found numerically
by means of the Fourier transform. An important ingredient of the linear medium
is the third-order dispersion, that eventually splits the array into individual
pulses. If the host medium is nonlinear, the input pulse is taken as a
fundamental soliton. The soliton is found to be much more resistant to the
action of the nonlinear defect than the Gaussian pulse in the linear host
medium. In this case, the third-order-dispersion splits the soliton proper and
wavepackets generated by the action of the defect.
