  We study systematically the scattering of solitons on localized impurities in
the discrete nonlinear Schr\"odinger (DNLS) equation with a saturable
nonlinearity. We show that, apart from the generic scenario of the outcome of
the scattering process, namely the emergence of a reflected and a transmitted
soliton, other effects can occur. In particular, it is found that, in the case
of an attractive impurity, a soliton trapped at the impurity can coexist with
the reflected and transmitted ones. This effect, which resembles the behaviour
of a quantum particle interacting with a narrow impurity, has not previously
reported for discrete setting. Parameter regimes are explored for determining
soliton splitting on the impurity with special attention to equal soliton
splitting.
