Simultaneous separation for the Neumann and Chaplygin systems
Exactly Solvable and Integrable Systems
2015-06-22 v2
Abstract
The Neumann and Chaplygin systems on the sphere are simultaneously separable in variables obtained from the standard elliptic coordinates by the proper Backlund transformation. We also prove that after similar Backlund transformations other curvilinear coordinates on the sphere and on the plane become variables of separations for the system with quartic potential, for the Henon-Heiles system and for the Kowalevski top. It allows us to say about some analog of the hetero Backlund transformations relating different Hamilton-Jacobi equations.
Keywords
Cite
@article{arxiv.1408.1198,
title = {Simultaneous separation for the Neumann and Chaplygin systems},
author = {A. V. Tsiganov},
journal= {arXiv preprint arXiv:1408.1198},
year = {2015}
}
Comments
21 pages, LaTeX with Amsfonts. arXiv admin note: text overlap with arXiv:nlin/0307021 by other authors