Mokhov, O. I. Nonlocal Hamiltonian operators of hydrodynamic type with flat metrics, and associativity equations. (English. Russian original) Zbl 1054.37042 Russ. Math. Surv. 59, No. 1, 191-192 (2004); translation from Usp. Mat. Nauk 59, No. 1, 187-188 (2004). From the introduction: We solve the problem of describing all nonlocal Hamiltonian operators of hydrodynamic type with flat metrics. It is proved that in a number of important cases such Hamiltonian operators are described by associativity equations and are closely related to the theory of Frobenius manifolds. We consider the important special case when the metric is flat. Cited in 1 Document MSC: 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) 37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry Keywords:integrable hierarchies; Frobenius manifolds PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 59, No. 1, 191--192 (2003; Zbl 1054.37042); translation from Usp. Mat. Nauk 59, No. 1, 187--188 (2004) Full Text: DOI