Solvable structures are particularly useful in the integration by quadratures of ordinary differential equations. Nevertheless, for a given equation, it is not always possible to compute a solvable structure. In practice, the simplest solvable structures are those adapted to an already known system of symmetries. In this paper we propose a method of integration which uses solvable structures suitably adapted to both symmetries and first integrals. In the variational case, due to Noether theorem, this method is particularly effective as illustrated by some examples of integration of the geodesic flows.
Integration of some examples of geodesic flows via solvable structures / D. Catalano Ferraioli, P. Morando. - In: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS. - ISSN 1402-9251. - 21:4(2014 Oct 14), pp. 521-532.
Integration of some examples of geodesic flows via solvable structures
D. Catalano Ferraioli;P. Morando
2014
Abstract
Solvable structures are particularly useful in the integration by quadratures of ordinary differential equations. Nevertheless, for a given equation, it is not always possible to compute a solvable structure. In practice, the simplest solvable structures are those adapted to an already known system of symmetries. In this paper we propose a method of integration which uses solvable structures suitably adapted to both symmetries and first integrals. In the variational case, due to Noether theorem, this method is particularly effective as illustrated by some examples of integration of the geodesic flows.File | Dimensione | Formato | |
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