We show how to construct the Hamiltonian structures of any reduction of the Benney chain (dispersionless KP). The construction follows the scheme suggested by Ferapontov, leading in general to nonlocal Hamiltonian structures. In some special cases these reduce to local structures. All the geometric objects which define the Poisson bracket, the metric, connection and Riemann curvature, are obtained explicitly, in terms of the n-parameter family of conformal maps associated with the reduction. © 2008 Springer-Verlag.
(2009). Hamiltonian structures of reductions of the Benney system [journal article - articolo]. In COMMUNICATIONS IN MATHEMATICAL PHYSICS. Retrieved from https://hdl.handle.net/10446/231049
Hamiltonian structures of reductions of the Benney system
Raimondo, A.
2009-01-01
Abstract
We show how to construct the Hamiltonian structures of any reduction of the Benney chain (dispersionless KP). The construction follows the scheme suggested by Ferapontov, leading in general to nonlocal Hamiltonian structures. In some special cases these reduce to local structures. All the geometric objects which define the Poisson bracket, the metric, connection and Riemann curvature, are obtained explicitly, in terms of the n-parameter family of conformal maps associated with the reduction. © 2008 Springer-Verlag.File | Dimensione del file | Formato | |
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