Scattering-induced splitting of solitons in the discrete NLS equation with saturable nonlinearity

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.