Is the Z2×Z2-graded sine-Gordon equation integrable?

Abstract

We examine the question of the integrability of the recently defined Z2×Z2-graded sine-Gordon model, which is a natural generalisation of the supersymmetric sine-Gordon equation. We do this via appropriate auto-Bäcklund transformations, construction of conserved spinor-valued currents and a pair of infinite sets of conservation laws.