Algebraic-geometry approach to construction

E. V. Glukhov ; O. I. Mokhov

Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1148-1160.

Résumé

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).

Détail

Keywords: Semi-Hamiltonian system, hydrodynamic type system, algebraic-geometric data, diagonal curvature metric, Baker–Akhiezer function.

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