Тип публикации: статья из журнала
Год издания: 2016
Идентификатор DOI: 10.1088/1751-8113/49/17/175201
Ключевые слова: geodesic flows, integrability, generalized hodograph method, 37J35, 37K05, 37K10, 70H05, generalized hodograph method Mathematics Subject Classification: 53D25
Аннотация: 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 derivedПоказать полностьюhydrodynamic-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.
Журнал: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Выпуск журнала: Vol. 49, Is. 17
ISSN журнала: 17518113
Место издания: BRISTOL
Издатель: IOP PUBLISHING LTD