Geodesic
Modifications of bundles, elliptic integrable systems, and related problems
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 3-67

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We describe a construction of elliptic integrable systems based on bundles with nontrivial characteristic classes, especially attending to the bundle-modification procedure, which relates models corresponding to different characteristic classes. We discuss applications and related problems such as the Knizhnik–Zamolodchikov–Bernard equations, classical and quantum $R$-matrices, monopoles, spectral duality, Painlevé equations, and the classical–quantum correspondence. For an $SL(N,\mathbb C)$-bundle on an elliptic curve with nontrivial characteristic classes, we obtain equations of isomonodromy deformations.
Keywords: integrable system, Painlevé equation, Hitchin system, modification of bundles. 
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     author = {A. V. Zotov and A. V. Smirnov},
     title = {Modifications of bundles, elliptic integrable systems, and related problems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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A. V. Zotov; A. V. Smirnov. Modifications of bundles, elliptic integrable systems, and related problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 3-67. http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a0/