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TMF, 2017, Volume 192, Number 3, Pages 473–488 (Mi tmf9286)  

This article is cited in 3 scientific papers (total in 3 papers)

Bäcklund transformations for the Jacobi system on an ellipsoid

A. V. Tsiganov

St. Petersburg State University, St. Petersburg, Russia

Abstract: We consider analogues of auto- and hetero-Bäcklund transformations for the Jacobi system on a three-axes 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.

Keywords: integrable system, Bäcklund transformation, Jacobi system on an ellipsoid.

Funding Agency Grant Number
Russian Science Foundation 15-11-30007
This research was supported by a grant from the Russian Science Foundation (Project No. 15-11-30007).


DOI: https://doi.org/10.4213/tmf9286

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English version:
Theoretical and Mathematical Physics, 2017, 192:3, 1350–1364

Bibliographic databases:

PACS: 02.30.Ik
MSC: 70E40 70H06
Received: 14.10.2016
Revised: 21.11.2016

Citation: A. V. Tsiganov, “Bäcklund transformations for the Jacobi system on an ellipsoid”, TMF, 192:3 (2017), 473–488; Theoret. and Math. Phys., 192:3 (2017), 1350–1364

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Tsiganov, “Backlund transformations and divisor doubling”, J. Geom. Phys., 126:SI (2018), 148–158  crossref  mathscinet  zmath  isi  scopus
    2. A. V. Tsiganov, “On exact discretization of cubic-quintic duffing oscillator”, J. Math. Phys., 59:7 (2018), 072703  crossref  mathscinet  zmath  isi  scopus
    3. A. V. Tsiganov, “Discretization of Hamiltonian systems and intersection theory”, Theoret. and Math. Phys., 197:3 (2018), 1806–1822  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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