Geodesic
Algebraic-geometry approach to construction
Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1148-1160

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In this paper, a class of semi-Hamiltonian diagonal systems of hydrodynamic type is constructed using algebraic-geometric methods. For such systems, hydrodynamic integrals and hydrodynamic symmetries are constructed from algebraic-geometric data. Besides, it is described what algebraic-geometric data distinguish in this class Hamiltonian diagonal systems with Hamiltonian structures defined by flat metrics (local Dubrovin–Novikov brackets) and metrics of constant curvature (nonlocal Mokhov–Ferapontov brackets).
Keywords: Semi-Hamiltonian system, hydrodynamic type system, algebraic-geometric data, diagonal curvature metric, Baker–Akhiezer function. 
@article{IM2_2023_87_6_a1,
     author = {E. V. Glukhov and O. I. Mokhov},
     title = {Algebraic-geometry approach to construction},
     journal = {Izvestiya. Mathematics },
     pages = {1148--1160},
     publisher = {mathdoc},
     volume = {87},
     number = {6},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a1/}
}
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E. V. Glukhov; O. I. Mokhov. Algebraic-geometry approach to construction. Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1148-1160. http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a1/