The non-autonomous YdKN equation and generalized symmetries of Boll equations

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 in the framework of the generalized Adler, Bobenko, and Suris (ABS) classification. 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 they pass the algebraic entropy test.