The negative symmetry classification problem

TL;DR

This paper introduces a method for constructing negative symmetries from differential equations and explores their relation to 3D consistent equations in both discrete and continuous cases.

Contribution

It presents a novel approach to generate negative symmetries using consistent triplets and analyzes their connection across discrete and continuous frameworks.

Findings

Method for constructing negative symmetries from triplets

Relation between 3D consistent discrete and continuous equations

Insights into nonlocal symmetry structures

Abstract

A negative symmetry is a nonlocal symmetry of special type. In this paper, we introduce a method for constructing negative symmetries from consistent triplets of differential and differential-difference equations. Moreover, we study the relation between 3D consistent equations in the discrete case and the continuous case.