Abstract
The goal of this Letter is to give a possibly simple and graphical description of the relationship between the isomonodromic problem and integrable systems. One can construct a huge integrable system which contains isomonodromic deformations as well as all known 2-dim integrable systems in the Zakharov–Shabat form as its restrictions. Besides, a proof of the isomonodromic property of the constructed deformations is given that is considerably easier than existent proofs.
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References
Jimbo, M., Miwa, T. and Ueno, K.: Monodromy preserving deformations of linear ordinary differential equations with rational coefficients, Physica D 2 (1981), 306–352.
Zakharov, V. E., Manakov, S. V., Novikov, S. P. and Pitaevski, L. P.: Theory of Solitons, Nauka, Moscow, 1980 (in Russian).
Dickey, L. A.: Additional symmetries of the Zakharov-Shabat hierarchy, string equation and isomonodromy, Lett. Math. Phys. 44 (1998), 53–65.
Dickey, L. A.: Why the Zakharov-Shabat equations form a hierarchy, Comm. Math. Phys. 163 (1994), 509–521.
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Dickey, L.A. Isomonodromic Deformations and Integrable Systems. Letters in Mathematical Physics 54, 165–179 (2000). https://doi.org/10.1023/A:1011041130474
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DOI: https://doi.org/10.1023/A:1011041130474