@article{b878ebdf41784e38bad0f8e268a0fa7f,
title = "Integrable geodesic flows on 2-torus: Formal solutions and variational principle",
abstract = "In this paper we study quasi-linear system of partial differential equations which describes the existence of the polynomial in momenta first integral of the integrable geodesic flow on 2-torus. We proved in Bialy and Mironov (2011) that this is a semi-Hamiltonian system and we show here that the metric associated with the system is a metric of Egorov type. We use this fact in order to prove that in the case of integrals of degree three and four the system is in fact equivalent to a single remarkable equation of order 3 and 4 respectively. Remarkably the equation for the case of degree four has variational meaning: it is Euler-Lagrange equation of a variational principle. Next we prove that this equation for n= 4 has formal double periodic solutions as a series in a small parameter.",
keywords = "Conservation laws, Geodesic flows, Integrable Hamiltonians, Semi-Hamiltonian systems",
author = "Misha Bialy and Mironov, {Andrey E.}",
note = "Publisher Copyright: {\textcopyright} 2014 Elsevier B.V.",
year = "2015",
month = jan,
day = "1",
doi = "10.1016/j.geomphys.2014.08.006",
language = "אנגלית",
volume = "87",
pages = "39--47",
journal = "Journal of Geometry and Physics",
issn = "0393-0440",
publisher = "Elsevier B.V.",
}