The associativity equations in the two-dimensional topological field theory as integrable Hamiltonian nondiagonalizable systems of hydrodynamic type

DOI10.1007/BF02509506zbMath0873.35090MaRDI QIDQ1357909

Evgeny V. Ferapontov, Oleg I. Mokhov

Publication date: 24 June 1997

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian propertysystems of hydrodynamic typeBäcklund type transformation

Mathematics Subject Classification ID

Related Items (19)

On the solutions to the Witten-Dijkgraaf-Verlinde-Verlinde associativity equations and their algebraic properties ⋮ The WDVV associativity equations as a high-frequency limit ⋮ Integrable structures for a generalized Monge-Ampère equation ⋮ Compatible metrics and the diagonalizability of nonlocally bi-Hamiltonian systems of hydrodynamic type ⋮ Note on generic singularities of planar flat 3-webs ⋮ Classification of the associativity equations possessing a Hamiltonian structure of Dubrovin–Novikov type ⋮ Duality for systems of conservation laws ⋮ Flat 3-webs via semi-simple Frobenius 3-manifolds ⋮ Darboux integrability for diagonal systems of hydrodynamic type ⋮ Algebraic-geometry approach to construction of semi-Hamiltonian systems of hydrodynamic type ⋮ Classification of the associativity equations with a first-order Hamiltonian operator ⋮ On the integrability of a third-order Monge-Ampère type equation. ⋮ WDVV equations and invariant bi-Hamiltonian formalism ⋮ Confluence of hypergeometric functions and integrable hydrodynamic-type systems ⋮ Projective-geometric aspects of homogeneous third-order Hamiltonian operators ⋮ Liouville integrability of the reduction of the associativity equations on the set of stationary points of an integral in the case of three primary fields ⋮ Linearly degenerate reducible systems of hydrodynamic type ⋮ Local classification of singular hexagonal 3-webs with holomorphic Chern connection form and infinitesimal symmetries ⋮ On the bi-Hamiltonian geometry of WDVV equations

Cites Work

• Differential geometry of nonlocal Hamiltonian operators of hydrodynamic type
• Bianchi transformation between the real hyperbolic Monge-Ampère equation and the Born-Infeld equation
• On integrability of \(3 \times{}3\) semi-Hamiltonian hydrodynamic type systems \(u_ t^ i = v_ j^ i (u) u_ x^ j\) which do not possess Riemann invariants
• Dupin hypersurfaces and integrable Hamiltonian systems of hydrodynamic type which do not possess Riemann invariants
• Several conjectures and results in the theory of integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants
• Non-local Hamiltonian operators of hydrodynamic type related to metrics of constant curvature
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
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