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An Integrable Discretization of the Rational \({\mathfrak su(2)}\) Gaudin Model and Related Systems

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Abstract

The first part of the present paper is devoted to a systematic construction of continuous-time finite-dimensional integrable systems arising from the rational \({\mathfrak su(2)}\) Gaudin model through certain contraction procedures. In the second part, we derive an explicit integrable Poisson map discretizing a particular Hamiltonian flow of the rational \({\mathfrak su(2)}\) Gaudin model. Then, the contraction procedures enable us to construct explicit integrable discretizations of the continuous systems derived in the first part of the paper.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, D-85747, Garching bei München, Germany

    Matteo Petrera & Yuri B. Suris

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  1. Matteo Petrera
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  2. Yuri B. Suris
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Correspondence to Yuri B. Suris.

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Communicated by L. Takhtajan

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Petrera, M., Suris, Y.B. An Integrable Discretization of the Rational \({\mathfrak su(2)}\) Gaudin Model and Related Systems. Commun. Math. Phys. 283, 227–253 (2008). https://doi.org/10.1007/s00220-008-0512-7

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