For construction and classification of the natural integrable systems we propose to use a criterion of separability in Darboux–Nijenhuis coordinates, which can be tested without an a priori explicit knowledge of these coordinates. As an example we apply this method for the search of integrable systems on the plane.
Keywords:
integrable systems, bi-Hamiltonian geometry, separation of variables
Citation:
Tsiganov A. V., Towards a classification of natural integrable systems , Regular and Chaotic Dynamics,
2006, Volume 11, Number 3,
pp. 343-362