The non autonomous YdKN equation and generalized symmetries of Boll equations

TL;DR

This paper investigates the integrability of non-autonomous quad graph equations introduced by Boll, demonstrating they possess generalized symmetries related to the Yamilov discretization of the Krichever–Novikov equation, and confirming their integrability via algebraic entropy.

Contribution

It establishes the existence of generalized symmetries for Boll's equations and proves their integrability, extending the understanding of non-autonomous integrable systems.

Findings

All equations have three-point generalized symmetries.

Symmetries are subcases of Yamilov discretization or its extension.

Equations pass the algebraic entropy test for integrability.

Abstract

In this paper we study the integrability of a class of nonlinear non autonomous quad graph equations compatible around the cube introduced by Boll. We show that all these equations possess three point generalized symmetries which are subcases of either the Yamilov discretization of the Krichever--Novikov equation or of its non autonomous extension. We also prove that all those symmetries are integrable as pass the algebraic entropy test.