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
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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.
@article{TMF_2023_216_2_a10,
author = {A. V. Tsiganov and E. O. Porubov},
title = {On a~class of quadratic conservation laws for {Newton} equations in {Euclidean} space},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {350--382},
publisher = {mathdoc},
volume = {216},
number = {2},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a10/}
}
TY - JOUR AU - A. V. Tsiganov AU - E. O. Porubov TI - On a~class of quadratic conservation laws for Newton equations in Euclidean space JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2023 SP - 350 EP - 382 VL - 216 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a10/ LA - ru ID - TMF_2023_216_2_a10 ER -
%0 Journal Article %A A. V. Tsiganov %A E. O. Porubov %T On a~class of quadratic conservation laws for Newton equations in Euclidean space %J Teoretičeskaâ i matematičeskaâ fizika %D 2023 %P 350-382 %V 216 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a10/ %G ru %F TMF_2023_216_2_a10
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/