Defects in the discrete non-linear Schrodinger model

TL;DR

This paper investigates the algebraic structure and integrability of the discrete non-linear Schrödinger model with an impurity, constructing conserved charges and Lax pairs, and exploring the continuum limit.

Contribution

It provides an algebraic framework for the NLS model with defects, explicitly constructing conserved quantities and Lax pairs, and analyzing the impurity's effects.

Findings

Explicit conserved charges in involution

Lax pairs incorporating defect terms

Insights into the continuum limit behavior

Abstract

The discrete non-linear Schrodinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.