  This paper concerns the scattering problem for a nonlinear medium of compact
support, $D$, with second-harmonic generation. Such a medium, when probed with
monochromatic light beams at frequency $\omega$, generates additional waves at
frequency $2\omega$. The response of the medium is governed by a system of two
coupled semilinear partial differential equations for the electric fields at
frequency $\omega$ and $2\omega$. We investigate whether there are situations
in which the generated $2\omega$ wave is localized inside $D$, that is, the
nonlinear interaction of the medium with the probing wave is invisible to an
outside observer. This leads to the analysis of a semilinear elliptic system
formulated in $D$ with non-standard boundary conditions. The analysis presented
here sets up a mathematical framework needed to investigate a multitude of
questions related to nonlinear scattering with second-harmonic generation.
