Lax pairs for the discrete reduced Nahm systems

Abstract

We discretise the Lax pair for the reduced Nahm systems and prove its equivalence with the Kahan-Hirota-Kimura discretisation procedure. We show that these Lax pairs guarantee the integrability of the discrete reduced Nahm systems providing an invariant. Also, we show with an example that Nahm systems cannot solve the general problem of characterisation of the integrability for Kahan-Hirota-Kimura discretisations.