Pairs of commuting Hamiltonians quadratic in momenta
Exactly Solvable and Integrable Systems
2008-02-13 v3
Abstract
In the case of two degree system the pairs of quadratic in momenta Hamiltonians commuting according the standard Poisson bracket are considered. The new many-parametrical families of such pairs are founded. The universal method of constructing the full solution of Hamilton - Jacobi equation in terms of integrals on some algebraic curve is proposed. For some examples this curve is non-hyperelliptic covering over the elliptic curve.
Keywords
Cite
@article{arxiv.0710.4035,
title = {Pairs of commuting Hamiltonians quadratic in momenta},
author = {V. G. Marikhin and V. V. Sokolov},
journal= {arXiv preprint arXiv:0710.4035},
year = {2008}
}
Comments
14 pages, proof of Theorem 1 added