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Bihamiltonian cohomologies and integrable hierarchies. I: A special case. (English) Zbl 1318.37019
The authors study the bi-Hamiltonian cohomologies associated with bi-Hamiltonian structures of hydrodynamic type, especially the third bi-Hamiltonian cohomology for the dispersionless KdV hierarchy. Using these results, they also study the deformation structure of the dispersionless KdV hierarchy and its bi-Hamiltonian structure, and prove a conjecture on the deformation by P. Lorenzoni [J. Geom. Phys. 44, No. 2–3, 331–375 (2002; Zbl 1010.37041)].

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)
53D40 Symplectic aspects of Floer homology and cohomology
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