A list of all integrable 2D homogeneous polynomial potentials with a polynomial integral of order at most 4 in the momenta

Details A list of all integrable 2D homogeneous polynomial potentials with a polynomial integral of order at most 4 in the momenta A list of all integrable 2D homogeneous polynomial potentials with a polynomial integral of order at most 4 in the momenta

2001-08-29

arxiv.org/abs/nlin/0108051v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages, no figures, to appear in J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/34/41/316

We searched integrable 2D homogeneous polynomial potential with a polynomial
first integral by using the so-called direct method of searching for first
integrals. We proved that there exist no polynomial first integrals which are
genuinely cubic or quartic in the momenta if the degree of homogeneous
polynomial potentials is greater than 4.

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