Bi-differential calculi and bi-Hamiltonian systems. (English) Zbl 0989.37063
Summary: We discuss the relationship between the analysis of completely integrable systems using bi-differential calculi which was introduced by A. Dimakis and F. Müller-Hoissen [Bi-differential calculi and integrable models, J. Phys. A, Math. Gen. 33, 957-974 (2000; Zbl 1043.37508)], and the bi-Hamiltonian formalism, in the finite-dimensional case.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 58B34 | Noncommutative geometry (à la Connes) |
