We study the Boussinesq hierarchy in the geometric context of the theory of bi-Hamiltonian manifolds. First, we recall how its bi-Hamiltonian structure can be obtained by means of a process called bi-Hamiltonian reduction, choosing a specific symplectic leaf of one of the two Poisson structures. Then, we introduce the notion of a bi-Hamiltonian S-hierarchy, that is, a bi-Hamiltonian hierarchy that is defined only at the points of the symplectic leaf S, and we show that the Boussinesq hierarchy can be interpreted as the reduction of a bi-Hamiltonian S-hierarchy.
(2021). Boussinesq hierarchy and bi-Hamiltonian geometry [journal article - articolo]. In JOURNAL OF MATHEMATICAL PHYSICS. Retrieved from http://hdl.handle.net/10446/200632
Boussinesq hierarchy and bi-Hamiltonian geometry
Pedroni, Marco
2021-01-01
Abstract
We study the Boussinesq hierarchy in the geometric context of the theory of bi-Hamiltonian manifolds. First, we recall how its bi-Hamiltonian structure can be obtained by means of a process called bi-Hamiltonian reduction, choosing a specific symplectic leaf of one of the two Poisson structures. Then, we introduce the notion of a bi-Hamiltonian S-hierarchy, that is, a bi-Hamiltonian hierarchy that is defined only at the points of the symplectic leaf S, and we show that the Boussinesq hierarchy can be interpreted as the reduction of a bi-Hamiltonian S-hierarchy.File | Dimensione del file | Formato | |
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