Geodesic
$1+1$ Gaudin Model
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study $1+1$ field-generalizations of the rational and elliptic Gaudin models. For ${\rm sl}(N)$ case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In ${\rm sl}(2)$ case we study the equations in detail and find the corresponding Hamiltonian densities. The $n$-site model describes $n$ interacting Landau–Lifshitz models of magnets. The interaction depends on position of the sites (marked points on the curve). We also analyze the $2$-site case in its own right and describe its relation to the principal chiral model. We emphasize that $1+1$ version impose a restriction on a choice of flows on the level of the corresponding $0+1$ classical mechanics.
Keywords: integrable systems; field theory; Gaudin models. 
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     author = {Andrei V. Zotov},
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}
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Andrei V. Zotov. $1+1$ Gaudin Model. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a66/

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