On local description of two-dimensional geodesic flows with a polynomial first integral dedicated to the 55th birthday of our friend E V Ferapontov

In this paper we present a construction of multiparametric families of two-dimensional metrics with a polynomial first integral of arbitrary degree in momenta. Such integrable geodesic flows are described by solutions of some semi-Hamiltonian hydrodynamic-type system. We give a constructive algorith...

Full description

Saved in:
Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 49; no. 17
Main Authors Pavlov, Maxim V, Tsarev, Sergey P
Format Journal Article
LanguageEnglish
Published IOP Publishing 18.03.2016
Subjects
generalized hodograph method
geodesic flows
integrability
Online AccessGet full text

Cover

More Information
Summary:In this paper we present a construction of multiparametric families of two-dimensional metrics with a polynomial first integral of arbitrary degree in momenta. Such integrable geodesic flows are described by solutions of some semi-Hamiltonian hydrodynamic-type system. We give a constructive algorithm for the solution of the derived hydrodynamic-type system, i.e. we found infinitely many conservation laws and commuting flows. Thus we were able to find infinitely many particular solutions of this hydrodynamic-type system by the generalized hodograph method. Therefore infinitely many particular two-dimensional metrics equipped with first integrals polynomial in momenta were constructed.
Bibliography:JPhysA-104477.R1
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/49/17/175201