Natural connections for semi-Hamiltonian systems: The case of the $\epsilon$-system

Abstract

Given a semi-Hamiltonian system, we construct an $F$-manifold with a connection satisfying a suitable compatibility condition with the product. We exemplify this procedure in the case of the so-called $\epsilon$-system. The corresponding connection turns out to be flat, and the flat coordinates give rise to additional chains of commuting flows

24 pages

References in corpus (5)

• Integrable hydrodynamic chains
• F-manifolds with flat structure and Dubrovin's duality
• Flat bidifferential ideals and semihamiltonian PDEs
• $F$-manifolds and integrable systems of hydrodynamic type
• A cohomological construction of integrable hierarchies of hydrodynamic type

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• Reciprocal $F$-manifolds
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