Algebraic-geometry approach to construction of semi-Hamiltonian systems of hydrodynamic type

DOI10.4213/im9303eOpenAlexW4390107270MaRDI QIDQ6184504

Unnamed Author, Oleg I. Mokhov

Publication date: 25 January 2024

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/im9303

zbMATH Keywords

Baker-Akhiezer functionhydrodynamic type systemsemi-Hamiltonian systemalgebraic-geometric datadiagonal curvature metric

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Relationships between algebraic curves and integrable systems (14H70) Local submanifolds (53B25)

Cites Work

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• Compatible metrics and the diagonalizability of nonlocally bi-Hamiltonian systems of hydrodynamic type
• On orthogonal curvilinear coordinate systems in constant curvature spaces
• Invariant integrability criterion for equations of hydrodynamic type
• Differential geometry of nonlocal Hamiltonian operators of hydrodynamic type
• The associativity equations in the two-dimensional topological field theory as integrable Hamiltonian nondiagonalizable systems of hydrodynamic type
• Bi-Hamiltonian structure of equations of associativity in 2-d topological field theory
• Algebraic-geometric \(n\)-orthogonal curvilinear coordinate systems and solutions of the associativity equations
• Classification of the associativity equations with a first-order Hamiltonian operator
• Description of the \(n\)-orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type. I: Integration of the Lamé equations
• On metrics of diagonal curvature
• Orthogonal curvilinear coordinate systems corresponding to singular spectral curves
• On algebraic-geometric methods for constructing submanifolds with flat normal bundle and holonomic net of curvature lines
• Riemann invariants of semisimple non-locally bi-Hamiltonian systems of hydrodynamic type and compatible metrics
• Non-local Hamiltonian operators of hydrodynamic type related to metrics of constant curvature
• Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems
• Pencils of compatible metrics and integrable systems
• Classification of the associativity equations possessing a Hamiltonian structure of Dubrovin–Novikov type
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
• On algebraic-geometry methods for constructing flat diagonal metrics of a special form

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