Difference integrability conditions for parameterized linear difference and differential equations

TL;DR

This paper establishes that for systems of linear difference and differential equations with parameters, being difference isomonodromic with respect to all parameters simultaneously is equivalent to being so with respect to each parameter individually, simplifying verification.

Contribution

It proves a key equivalence in integrability conditions for parameterized systems, reducing complex non-linear problem solving to simpler checks per parameter.

Findings

Equivalence of difference isomonodromicity across all parameters and individually.

Simplification of verifying integrability conditions.

Enhanced computational efficiency for analyzing such systems.

Abstract

This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference isomonodromic with respect to each parameter separately. Due to this result, it is no longer necessary to solve non-linear difference equations to verify isomonodromicity, which will improve efficiency of computation with these systems.