  Investigations of scattering in presence of non-linearity which have just
begun require the confinement of both the potential, $V(x)$, and the
non-linearity, $\gamma f(|\psi|)$. There could be two options for the
confinement. One is the finite support on $x \in [-L,L]$ and the other one is
on $x \in [0,L]$. Here, we consider real Hermitian potentials and report a
surprising disparate behaviour of these two types of confinements. We prove
that in the first option the symmetric potential enjoys reciprocity of both
reflectivity ($R$) and transmitivity ($T$) and their unitarity. More
interestingly, the asymmetry in $V(x)$ causes non-unitarity ($ R+T\ne 1$) and
the non-reciprocity (reciprocity) of $T (R)$. On the other hand, the second
option of confinement gives rise to an essential non-unitarity even when $V(x)$
is symmetric about a point in $[0,L]$. In the absence of symmetry there occurs
non-reciprocity of both $R$ and $T$.
