Geodesic
On a class of quadratic conservation laws for Newton equations in Euclidean space
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 350-382 Cet article a éte moissonné depuis la source Math-Net.Ru

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We discuss quadratic conservation laws for the Newton equations and the corresponding second-order Killing tensors in Euclidean space. In this case, the complete set of integrals of motion consists of polynomials of the second, fourth, sixth, and so on degrees in momenta, which can be constructed using the Lax matrix related to the hierarchy of the multicomponent nonlinear Schrödinger equation.
Keywords: Killing tensors, integrable systems, symmetric spaces. 
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A. V. Tsiganov; E. O. Porubov. On a class of quadratic conservation laws for Newton equations in Euclidean space. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 350-382. http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a10/

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