TY - JOUR

T1 - Bäcklund transformations for the Jacobi system on an ellipsoid

AU - Tsiganov, A. V.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - We consider analogues of auto- and hetero-Bäcklund transformations for the Jacobi system on a threeaxis ellipsoid. Using the results in a Weierstrass paper, where the change of times reduces integrating the equations of motion to inverting the Abel mapping, we construct the differential Abel equations and auto-Bäcklund transformations preserving the Poisson bracket with respect to which the equations of motion written in the Weierstrass form are Hamiltonian. Transforming this bracket to the canonical form, we can construct a new integrable system on the ellipsoid with a Hamiltonian of the natural form and with a fourth-degree integral of motion in momenta.

AB - We consider analogues of auto- and hetero-Bäcklund transformations for the Jacobi system on a threeaxis ellipsoid. Using the results in a Weierstrass paper, where the change of times reduces integrating the equations of motion to inverting the Abel mapping, we construct the differential Abel equations and auto-Bäcklund transformations preserving the Poisson bracket with respect to which the equations of motion written in the Weierstrass form are Hamiltonian. Transforming this bracket to the canonical form, we can construct a new integrable system on the ellipsoid with a Hamiltonian of the natural form and with a fourth-degree integral of motion in momenta.

KW - Bäcklund transformation

KW - integrable system

KW - Jacobi system on an ellipsoid

UR - http://www.scopus.com/inward/record.url?scp=85030149440&partnerID=8YFLogxK

U2 - 10.1134/S0040577917090069

DO - 10.1134/S0040577917090069

M3 - Article

AN - SCOPUS:85030149440

VL - 192

SP - 1350

EP - 1364

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 3

ER -