Pairs of commuting Hamiltonians quadratic in momenta

Details Pairs of commuting Hamiltonians quadratic in momenta Pairs of commuting Hamiltonians quadratic in momenta

2007-10-22

arxiv.org/abs/0710.4035v3

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, proof of Theorem 1 added

Scientific paper

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.

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