Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras | Zendy

A.A. Gainetdinova | Zendy; Р. К. Газизов | Zendy

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Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras

Author(s) -

A.A. Gainetdinova,

Р. К. Газизов

Publication year - 2017

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2016.0461

Subject(s) - mathematics , ordinary differential equation , transformation group , invariant (physics) , homogeneous space , differential operator , pure mathematics , lie group , differential equation , mathematical analysis , algebra over a field , mathematical physics , geometry

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.

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