Reduction of Time-Dependent Systems Admitting a Superposition Principle

@article{Cariena2001ReductionOT,
  title={Reduction of Time-Dependent Systems Admitting a Superposition Principle},
  author={Jos{\'e} F. Cari{\~n}ena and Janusz Grabowski and A. Orfila Ramos},
  journal={Acta Applicandae Mathematica},
  year={2001},
  volume={66},
  pages={67-87}
}
The problem of differential equation systems admitting a nonlinear superposition principle is analyzed from a geometric perspective. We show how it is possible to reduce the problem of finding the general solution of such a differential equation system defined by a Lie group G to a pair of simpler problems, one in a subgroup H and the other on a homogeneous space. The theory is illustrated with several examples and applications. 

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