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• W1659926941 abstract "We consider some differential geometric classes of local and nonlocal Poisson and symplectic structures on loop spaces of smooth manifolds which give natural Hamiltonian and multihamiltonian representations for some important nonlinear equations of mathematical physics and field theory such as nonlinear sigma models with torsion, degenerate Lagrangian systems of field theory, systems of hydrodynamic type, N-component systems of Heisenberg magnet type, Monge-Amp`ere equations, the Krichever-Novikov equation and others. In addition, we shall prove integrability of some class of nonhomogeneous systems of hydrodynamic type and give a description of nonlinear partial differential equations of associativity in $2D$ topological field theories (for some special type solutions of the Witten-Dijkgraaf-E.Verlinde-H.Verlinde (WDVV) system) as integrable nondiagonalizable weakly nonlinear homogeneous systems of hydrodynamic type." @default.
• W1659926941 created "2016-06-24" @default.
• W1659926941 creator A5049028698 @default.
• W1659926941 date "1995-09-13" @default.
• W1659926941 modified "2023-09-23" @default.
• W1659926941 title "Symplectic and Poisson geometry on loop spaces of manifolds and nonlinear equations" @default.
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• W1659926941 doi "https://doi.org/10.1090/trans2/170/06" @default.
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