Geodesic
The Bi-Hamiltonian Theory of the Harry Dym Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 311-326 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: $bi$-Hamiltonian formalism, Harry Dym equation, completely integrable systems. 
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M. Pedroni; V. Sciacca; J. P. Zubelli. The Bi-Hamiltonian Theory of the Harry Dym Equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 311-326. http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a15/

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