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

TL;DR

This paper systematically investigates how solitons scatter off localized impurities in the discrete nonlinear Schrödinger equation with saturable nonlinearity, revealing novel trapping phenomena and conditions for soliton splitting.

Contribution

It introduces the first report of soliton trapping at an impurity in a discrete setting and explores parameter regimes for soliton splitting, including equal splitting.

Findings

Solitons can be reflected, transmitted, or trapped by impurities.

Trapping of solitons at an impurity can coexist with reflection and transmission.

Parameter regimes for equal soliton splitting are identified.

Abstract

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.