Topological Solitons Seminar: "Alternative Hamiltonian formalism relatively to Dubrovin-Novikov type."
30 January 2002 13:00 in CM221
"Local Hamiltonian structures determined by flat metric (Dubrovin-Novikov type) and nonlocal Hamiltonian structures determined by metric with flat normal bundle (Ferapontov type) were established at 1983 and at 1991, respectively.
We start from Lagrangian approach determine integrable hydrodynamic type systems. In this case we establish new type of nonlocal Hamiltonian structures.
Most interesting feauture is that many very well known famous and significant systems have abovementioned description, like ideal gas dynamics.
Moreover, in Egorov case we could prove that these systems have infinite set of local Hamiltonian structures (not Dubrovin-Novikov type). One problem is still open: we do not know geometrical interpretation of these Hamiltonian structures, but central place in this theory is metric like in classical (Dubrovin-Novikov-Ferapontov)."
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