Hamiltonian systems of hydrodynamic type and their realization on hypersurfaces of a pseudo-Euclidean space

DOI10.1007/BF01095672zbMath0741.58016OpenAlexW2049247619MaRDI QIDQ1180290

Evgeny V. Ferapontov

Publication date: 27 June 1992

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01095672

zbMATH Keywords

Hamiltonian systemshypersurfaces of a pseudo-Euclidean space

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) PDEs in connection with fluid mechanics (35Q35) Gas dynamics (general theory) (76N15) Applications of manifolds of mappings to the sciences (58D30) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Spectral theory; eigenvalue problems on manifolds (58C40)

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Cites Work

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• Compact Dupin hypersurfaces with three principal curvatures
• The Hamilton property of stationary and inverse equations of condensed matter mechanics and mathematical physics
• Mathematics of dispersive water waves
• Non-local Hamiltonian operators of hydrodynamic type related to metrics of constant curvature
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• The geometry of conservative systems of hydrodynamic type. The method of averaging for field-theoretical systems
• On a new class of completely integrable nonlinear wave equations. II. Multi-Hamiltonian structure
• Diagonalization and Hamiltonian structures of hyperbolic systems