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This article is cited in 16 scientific papers (total in 16 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.
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
Linking options:
https://www.mathnet.ru/eng/tmf9286https://doi.org/10.4213/tmf9286 https://www.mathnet.ru/eng/tmf/v192/i3/p473
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Abstract page: | 354 | Full-text PDF : | 104 | References: | 36 | First page: | 12 |
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