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- W3100304920 abstract "We consider a lattice ℒ ⊂ ℝ n and a trigonometric potential V with frequencies k ∈ ℒ. We then prove a strong rational integrability condition on V, using the support of its Fourier transform. We then use this condition to prove that a real trigonometric polynomial potential is rationally integrable if and only if it separates up to rotation of the coordinates. Removing the real condition, we also make a classification of rationally integrable potentials in dimensions 2 and 3 and recover several integrable cases. After a complex change of variables, these potentials become real and correspond to generalized Toda integrable potentials. Moreover, along the proof, some of them with high-degree first integrals are explicitly integrated." @default.
- W3100304920 created "2020-11-23" @default.
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- W3100304920 date "2017-07-01" @default.
- W3100304920 modified "2023-10-01" @default.
- W3100304920 title "Rational integrability of trigonometric polynomial potentials on the flat torus" @default.
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- W3100304920 doi "https://doi.org/10.1134/s1560354717040049" @default.
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