# Integrable 7-point discrete equations and evolution lattice equations of order 2

## TL;DR

This paper explores the connection between differential-difference equations and discrete equations on a triangular lattice, demonstrating how certain symmetries can be represented as second-order scalar evolution lattice equations, with examples including elliptic Yamilov lattice.

## Contribution

It introduces a method to represent continuous symmetries of discrete lattice equations as second-order evolution lattice equations, expanding understanding of integrable discrete systems.

## Key findings

- A scalar evolution lattice equation of order 2 can represent combined continuous flows.
- Examples include an analog of the elliptic Yamilov lattice equation.
- The approach links differential-difference equations with integrable discrete equations.

## Abstract

We consider differential-difference equations that determine the continuous symmetries of discrete equations on the triangular lattice. It is shown that a certain combination of continuous flows can be represented as a scalar evolution lattice equation of order 2. The general scheme is illustrated by a number of examples, including an analog of the elliptic Yamilov lattice equation.