TY - JOUR

T1 - Hydrodynamic-type systems describing 2-dimensional polynomially integrable geodesic flows

AU - Manno, Gianni

AU - Pavlov, Maxim V.

N1 - Publisher Copyright: © 2016 Elsevier B.V.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 2-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type systems are semi-Hamiltonian, thus implying that they are integrable according to the generalized hodograph method. Moreover, they are integrable in a constructive sense as polynomial first integrals allow to construct generating equations of conservation laws. According to the multiplicity of the roots of the polynomial integral, we separate integrable particular cases.

AB - Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 2-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type systems are semi-Hamiltonian, thus implying that they are integrable according to the generalized hodograph method. Moreover, they are integrable in a constructive sense as polynomial first integrals allow to construct generating equations of conservation laws. According to the multiplicity of the roots of the polynomial integral, we separate integrable particular cases.

KW - Integrable geodesic flows

KW - Semi-Hamiltonian hydrodynamic systems

KW - METRICS

UR - http://www.scopus.com/inward/record.url?scp=85007591233&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2016.10.023

DO - 10.1016/j.geomphys.2016.10.023

M3 - Article

AN - SCOPUS:85007591233

VL - 113

SP - 197

EP - 205

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

ER -