A new class of integrable systems
- 1 September 1983
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 24 (9) , 2282-2288
- https://doi.org/10.1063/1.525975
Abstract
We present a family of dynamical systems associated with the motion of a particle in two space dimensions. These systems possess a second integral of motion quadratic in velocities (apart from the Hamiltonian) and are thus completely integrable. They were found through the derivation and subsequent resolution of the integrability condition in the form of a partial differential equation (PDE) for the potential. A most important point is that the same PDE was derived through considerations on the analytic structure of the singularities of the solutions (‘‘weak-Painlevé property’’).Keywords
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