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Reduction of the 2D Toda Hierarchy and Linear Hodge Integrals
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct a certain reduction of the 2D Toda hierarchy and obtain a tau-symmetric Hamiltonian integrable hierarchy. This reduced integrable hierarchy controls the linear Hodge integrals in the way that one part of its flows yields the intermediate long wave hierarchy, and the remaining flows coincide with a certain limit of the flows of the fractional Volterra hierarchy which controls the special cubic Hodge integrals.
Keywords: integrable hierarchy, limit fractional Volterra hierarchy, intermediate long wave hierarchy. 
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     author = {Si-Qi Liu and Zhe Wang and Youjin Zhang},
     title = {Reduction of the {2D} {Toda} {Hierarchy} and {Linear} {Hodge} {Integrals}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a36/}
}
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Si-Qi Liu; Zhe Wang; Youjin Zhang. Reduction of the 2D Toda Hierarchy and Linear Hodge Integrals. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a36/

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