A Darboux theorem for Hamiltonian operators in the formal calculus of variations. (English) Zbl 1100.32008

The author proves a formal Darboux type theorem for Hamiltonian operators of hydrodynamic type, which arise as dispersionless limits of the Hamiltonian operators in the KdV and similar hierarchies. It is shown that the Schouten Lie algebra is a formal differential graded Lie algebra. An exposition is included of the formal deformation theory of differential graded Lie algebras concentrated in degrees \([-1,\infty )\).


32G34 Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation)
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
35Q53 KdV equations (Korteweg-de Vries equations)
55P62 Rational homotopy theory
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