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.

Gibbons, J., Lorenzoni, P., & Raimondo, A. (2009). Hamiltonian structures of reductions of the Benney system. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 287(1), 291-322 [10.1007/s00220-008-0686-z].

Hamiltonian structures of reductions of the Benney system

LORENZONI, PAOLO;RAIMONDO, ANDREA
2009

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.
Si
Articolo in rivista - Articolo scientifico
Scientifica
Hamiltonian structures of hydrodynamic typre; KP hierarchy
English
Gibbons, J., Lorenzoni, P., & Raimondo, A. (2009). Hamiltonian structures of reductions of the Benney system. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 287(1), 291-322 [10.1007/s00220-008-0686-z].
Gibbons, J; Lorenzoni, P; Raimondo, A
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/5677
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