Construction of Solvable Structures from \(\mathfrak {so}(3,\mathbb {C})\)

  • A. RuizEmail author
  • C. MurielEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 266)


For third-order ordinary differential equations admitting a Lie symmetry algebra isomorphic to \(\mathfrak {so}(3,\mathbb {C})\) it is proved the existence of a solvable structure constructed out of the symmetry generators of the algebra. This solvable structure is explicitly obtained in terms of solutions to a second-order linear ordinary differential equation. Once the solvable structure is known, a complete set of first integrals can be computed by quadratures. Moreover, it is proved that the general solution can be obtained in parametric form and expressed in terms of solutions to a second-order linear equation.


First integral Solvable structure Non-solvable symmetry algebra 



The authors acknowledge the financial support from the University of Cádiz by means of the project PR2017-090 and from the Junta de Andalucía research group FQM-377.

A. Ruiz acknowledges the financial support from the Ministry of Education, Culture and Sport of Spain (FPU grant FPU15/02872).


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CádizPuerto RealSpain

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