Lax Pairs for the Discrete Reduced Nahm Systems

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 that Nahm systems cannot solve the general problem of characterisation of the integrability for Kahan-Hirota-Kimura discretisations.

Automated summary

The discretisation of the reduced Nahm systems using Lax pair is proven to be equivalent to the Kahan-Hirota-Kimura discretisation method. It is demonstrated that the Lax pairs ensure the integrability of the discrete reduced Nahm systems, but they cannot provide a solution to the general problem of characterisation of integrability for Kahan-Hirota-Kimura discretisations.