# From discrete nonlocal nonlinear Schr\"odinger equation to coupled discrete Heisenberg ferromagnet equation

## TL;DR

This paper establishes a gauge equivalence between nonlocal discrete nonlinear Schrödinger equations and coupled Heisenberg ferromagnet equations, linking their solutions through continuous limits and providing new insights into their relationships.

## Contribution

It demonstrates the gauge equivalence between nonlocal discrete NLS equations and coupled Heisenberg ferromagnet equations, and derives solutions via this connection.

## Key findings

- Nonlocal discrete focusing and defocusing NLS are gauge equivalent to coupled HF equations.
- Continuous limits of these equations lead to their classical counterparts.
- Solutions of the modified coupled HF are obtained from nonlocal defocusing NLS solutions.

## Abstract

In this paper, we show that the nonlocal discrete focusing nonlinear Schr\"odinger (NLS) and nonlocal discrete defocusing NLS equation are gauge equivalent to the discrete coupled Heisenberg ferromagnet (HF) equation and the discrete modified coupled HF equation, respectively. Under the continuous limit, the discrete coupled HF equation and the modified discrete coupled HF equation lead to the corresponding coupled HF equation and modified coupled HF equation. This means that the nonlocal focusing and defocusing NLS equations are gauge equivalent to the coupled HF and coupled modified HF equations. The solution of the modified coupled HF equation is obtained by using the solution of nonlocal defocusing NLS equation.