The bi-Hamiltonian theory of the Harry Dym equation
- Autori: Pedroni, M.; Sciacca, V.; Zubelli, J.;
- Anno di pubblicazione: 2002
- Tipologia: Articolo in rivista (Articolo in rivista)
- OA Link: http://hdl.handle.net/10447/107229
Abstract
We describe how the Harry Dym equation fits into the the bi-Hamiltonian formalism for the Korteweg-de Vries equation and other soliton equations. This is achieved using a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue of the Kadomtsev-Petviashivili hierarchy whose reduction leads to the Harry Dym hierarchy. We call such a system the HD-KP hierarchy. We then construct an infinite system of ordinary differential equations (in infinitely many variables) that is equivalent to the HD-KP hierarchy. Its role is analogous to the role of the Central System in the Kadomtsev-Petviashivili hierarchy.