Semi-discrete hyperbolic equations admitting five dimensional characteristic $x$-ring

TL;DR

This paper derives conditions under which semi-discrete hyperbolic equations possess a five-dimensional characteristic x-ring, providing a straightforward way to verify these conditions for any given chain.

Contribution

It establishes necessary and sufficient conditions for the existence of a five-dimensional characteristic x-ring in semi-discrete hyperbolic equations, enhancing understanding of their symmetry properties.

Findings

Derived verifiable conditions for five-dimensional x-rings

Applicable to any given semi-discrete hyperbolic chain

Simplifies analysis of symmetry structures in such equations

Abstract

The necessary and sufficient conditions for a hyperbolic semi-discrete equation to have five dimensional characteristic {\it x}-ring are derived. For any given chain, the derived conditions are easily verifiable by straightforward calculations.