Symmetries and First Integrals of Differential Equations

• Autores: Jing Zhang, Yong Li
• Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 103, Nº. 2, 2008, págs. 147-159
• Idioma: inglés
• DOI: 10.1007/s10440-008-9226-2
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• Resumen

  • It is known that an n-dimensional system of ordinary differential equations with Lie symmetry which involves a divergence-free Liouville vector field possesses n-1 independent first integrals (i.e., it is algebraically integrable) (Ünal in Phys. Lett. A 260:352�359, [1999]). In the present paper, we show that if an n-dimensional system of ordinary differential equations admits a C ?-symmetry vector field which satisfies some special conditions, then it also possesses n-1 independent first integrals. Several examples are given to illustrate our result.