Interaction of discrete nonlinear Schr\"odinger solitons with a linear lattice impurity

TL;DR

This paper studies how discrete nonlinear Schrödinger solitons interact with linear impurities, revealing conditions for transmission, reflection, and splitting, supported by analytical and numerical methods.

Contribution

It provides new insights into soliton-impurity interactions, including conditions for soliton transmission, reflection, and splitting, with analytical predictions validated by numerical simulations.

Findings

Existence of transmission and reflection windows depending on soliton amplitude.

Critical impurity strength causes soliton splitting into two parts.

Good agreement between analytical predictions and numerical simulations.

Abstract

The interaction of moving discrete solitons with a linear Gaussian defect is investigated. Solitons with profiles varying from hyperbolic secant to exponentially localized are considered such that the mobility of soliton is maintained; the condition for which is obtained. Studies on scattering of the soliton by an attractive defect potential reveal the existence of total reflection and transmission windows which become very narrow with increasing initial soliton amplitude. Transmission regions disappear beyond the small-amplitude limit. The regions of complete reflection and partial capture correspond to the windows of the existence and nonexistence of solution of the stationary problem. Interaction of the discrete soliton with a barrier potential is also investigated. The critical amplitude of the defect at which splitting of the soliton into two parts occurs was estimated from a balance equation. The results were confirmed through direct numerical integration of the dynamical equation showing very good agreement with the analytical prediction.