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.
Lax Pairs for the Discrete Reduced Nahm Systems / G. Gubbiotti. - In: MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY. - ISSN 1385-0172. - 24:2(2021 Mar 18), pp. 9.1-9.13. [10.1007/s11040-021-09381-7]
Lax Pairs for the Discrete Reduced Nahm Systems
G. Gubbiotti
2021
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 that Nahm systems cannot solve the general problem of characterisation of the integrability for Kahan–Hirota–Kimura discretisations.
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