Geodesic
The reduction of the second and third order differential equations which admit Lie algebra
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2009), pp. 69-73

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In the published work, the reduction of differential equations which admit Lie algebra is presented. The differential equation of the second order which admits Lie algebra and reducted groups which are set by local point operator and exponential nonlocal operator are researched. In case of the differential equation of the third order which admits unsolvable Lie algebra, the reducted groups which are admitted by local points operators as well as non-local operators are viewed.
Keywords: differential equation, differential equation of the second order, differential equation of the third order, Lie algebra, local operator, exponential nonlocal operator. 
@article{VSGU_2009_6_a6,
     author = {Yu. O. Yakovleva},
     title = {The reduction of the second and third order differential equations which admit {Lie} algebra},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {69--73},
     publisher = {mathdoc},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2009_6_a6/}
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Yu. O. Yakovleva. The reduction of the second and third order differential equations which admit Lie algebra. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2009), pp. 69-73. http://geodesic.mathdoc.fr/item/VSGU_2009_6_a6/