Standard

Separation of variables for a pair of integrable systems on so*(4). / Tsiganov, A. V.

In: Doklady Mathematics, Vol. 76, No. 3, 12.2007, p. 839-842.

Research output: Contribution to journal › Article › peer-review

Harvard

Tsiganov, AV 2007, 'Separation of variables for a pair of integrable systems on so*(4)', Doklady Mathematics, vol. 76, no. 3, pp. 839-842. https://doi.org/10.1134/S1064562407060099

APA

Tsiganov, A. V. (2007). Separation of variables for a pair of integrable systems on so*(4). Doklady Mathematics, 76(3), 839-842. https://doi.org/10.1134/S1064562407060099

Vancouver

Tsiganov AV. Separation of variables for a pair of integrable systems on so*(4). Doklady Mathematics. 2007 Dec;76(3):839-842. https://doi.org/10.1134/S1064562407060099

Author

Tsiganov, A. V. / Separation of variables for a pair of integrable systems on so*(4). In: Doklady Mathematics. 2007 ; Vol. 76, No. 3. pp. 839-842.

BibTeX

@article{438997825be44ff3a247baad7c6b8462,
title = "Separation of variables for a pair of integrable systems on so*(4)",
abstract = "A bi-Hamiltonian structure and separation variables are found for a pair of integrable systems on the Poisson manifold with quadratic Hamiltonians and second integrals of motion that are third- and fourth-degree polynomials. The compatible Poisson bivectors are constructed on Poisson manifold in the class of quadratic Poisson tensors and the separation of variables for the corresponding bi-integrable systems possessing higher degree integrals of motion is discussed. The Poisson bivectors are degenerate and need a special reduction to integrate the equations of motions. It is more convenient to use the coordinates to obtain a more compact description of the corresponding integrable systems. Quadratic linear integrals of motion are found in bi-involution with respect to the Poisson bracket associated with the bivectors and with the quadratic linear tensor.",
author = "Tsiganov, {A. V.}",
year = "2007",
month = dec,
doi = "10.1134/S1064562407060099",
language = "English",
volume = "76",
pages = "839--842",
journal = "Doklady Mathematics",
issn = "1064-5624",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "3",

}

RIS

TY - JOUR

T1 - Separation of variables for a pair of integrable systems on so*(4)

AU - Tsiganov, A. V.

PY - 2007/12

Y1 - 2007/12

N2 - A bi-Hamiltonian structure and separation variables are found for a pair of integrable systems on the Poisson manifold with quadratic Hamiltonians and second integrals of motion that are third- and fourth-degree polynomials. The compatible Poisson bivectors are constructed on Poisson manifold in the class of quadratic Poisson tensors and the separation of variables for the corresponding bi-integrable systems possessing higher degree integrals of motion is discussed. The Poisson bivectors are degenerate and need a special reduction to integrate the equations of motions. It is more convenient to use the coordinates to obtain a more compact description of the corresponding integrable systems. Quadratic linear integrals of motion are found in bi-involution with respect to the Poisson bracket associated with the bivectors and with the quadratic linear tensor.

AB - A bi-Hamiltonian structure and separation variables are found for a pair of integrable systems on the Poisson manifold with quadratic Hamiltonians and second integrals of motion that are third- and fourth-degree polynomials. The compatible Poisson bivectors are constructed on Poisson manifold in the class of quadratic Poisson tensors and the separation of variables for the corresponding bi-integrable systems possessing higher degree integrals of motion is discussed. The Poisson bivectors are degenerate and need a special reduction to integrate the equations of motions. It is more convenient to use the coordinates to obtain a more compact description of the corresponding integrable systems. Quadratic linear integrals of motion are found in bi-involution with respect to the Poisson bracket associated with the bivectors and with the quadratic linear tensor.

UR - http://www.scopus.com/inward/record.url?scp=37849044835&partnerID=8YFLogxK

U2 - 10.1134/S1064562407060099

DO - 10.1134/S1064562407060099

M3 - Article

AN - SCOPUS:37849044835

VL - 76

SP - 839

EP - 842

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 3

ER -

ID: 8484292