How to construct finite-dimensional bi-Hamiltonian systems from soliton equations: Jacobi integrable potentials
- 1 June 1992
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 33 (6), 2115-2125
- https://doi.org/10.1063/1.529632
Abstract
A systematic method of constructing finite‐dimensional integrable systems starting from a bi‐Hamiltonian hierarchy of soliton equations is introduced. The existence of two Hamiltonian structures of the hierarchy leads to a bi‐Hamiltonian formulation of the resulting finite‐dimensional systems. The case of coupled KdV hierarchies is studied in detail. A surprising connection with separable Jacobi potentials is uncovered and described.Keywords
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