On Lie systems and Kummer-Schwarz equations

@article{Lucas2013OnLS,
  title={On Lie systems and Kummer-Schwarz equations},
  author={Javier de Lucas and Cristina Sard{\'o}n},
  journal={Journal of Mathematical Physics},
  year={2013},
  volume={54},
  pages={033505}
}
  • Javier de Lucas, Cristina Sardón
  • Published 2013
  • Physics, Mathematics
  • Journal of Mathematical Physics
  • A Lie system is a system of first-order differential equations admitting a superposition rule, i.e., a map that expresses its general solution in terms of a generic family of particular solutions and certain constants. In this work, we use the geometric theory of Lie systems to prove that the explicit integration of second- and third-order Kummer-Schwarz equations is equivalent to obtaining a particular solution of a Lie system on SL(2,R). This same result can be extended to Riccati, Milne… CONTINUE READING

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