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.
|Numero di pagine||13|
|Rivista||Theoretical and Mathematical Physics|
|Stato di pubblicazione||Published - 2002|
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