Geodesic
Nonlocal symmetries and reductions for some ordinary differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 428-437

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We derive nonlocal symmetries for ordinary differential equations (ODEs). These symmetries are derived by embedding the ODE in an auxiliary system. Using these symmetries, we find that the order of the ODE can be reduced even if it does not admit point symmetries.
Keywords: conditional symmetry, nonlocal symmetry, ordinary differential equation. 
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     author = {M. L. Gandarias},
     title = {Nonlocal symmetries and reductions for some ordinary differential equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {428--437},
     publisher = {mathdoc},
     volume = {159},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a9/}
}
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M. L. Gandarias. Nonlocal symmetries and reductions for some ordinary differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 428-437. http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a9/