A non autonomous generalization of the $Q_{\text{V}}$ equation

TL;DR

This paper introduces a non-autonomous generalization of the QV equation, unifying various equations in Boll's classification, and provides evidence of its integrability through algebraic entropy and symmetries.

Contribution

It presents a new non-autonomous version of the QV equation that encompasses known equations and analyzes its integrability properties.

Findings

Equation appears integrable based on algebraic entropy

Identifies three-point generalized symmetries

Unifies equations in Boll's classification

Abstract

In this paper we introduce a non autonomous generalization of the $\QV$ equation introduced by Viallet. All the equations of Boll's classification appear in it for special choices of the parameters. Using the algebraic entropy test we infer that the equation should be integrable and with the aid of a formula introduced by Xenitidis we find its three point generalized symmetries.