Hamiltonians separable in cartesian coordinates and third-order integrals of motion
Gravel, Simon
arXiv, 0302028 / Harvested from arXiv
Text on arXiv
We present in this article all Hamiltonian systems in E(2) that are separable in cartesian coordinates and that admit a third-order integral, both in quantum and in classical mechanics. Many of these superintegrable systems are new, and it is seen that there exists a relation between quantum superintegrable potentials, invariant solutions of the Korteweg-De Vries equation and the Painlev\'e transcendents.
Publié le : 2003-02-11
Classification:  Mathematical Physics,  Mathematics - Dynamical Systems 
@article{0302028,
     author = {Gravel, Simon},
     title = {Hamiltonians separable in cartesian coordinates and third-order
  integrals of motion},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0302028}
}

Gravel, Simon. Hamiltonians separable in cartesian coordinates and third-order
  integrals of motion. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0302028/